The original reason that the FAA decided to establish (E4) surface-level Class E "extensions" to Class D (or higher) airspace was unambiguously to protect the airspace to the surface, while relieving VFR pilots passing through the airspace of the need to communicate with the control tower. From the May 1 1992 Proposed Rule "Terminal Airspace Reconfiguration", page 18958: "If these extensions were designated as Class E airspace areas, pilots who operate in the extension areas would not be required to contact the air traffic control facility having jurisdiction in those areas." And from the August 27 1992 Final Rule "Terminal Airspace Reconfiguration", page 38964: "By designating these extension areas as Class E airspace, pilots who operate in the extension areas will not be required to contact the air traffic control facility having jurisdiction over those areas."
Keep in mind that prior to the September 16 1993 "alphabet" airspace re-organization, surface-level airspace was protected by "control zones", which after September 16 1993 were transformed into surface-level Class E airspace at untowered airports, and surface-level Class D (and higher) airspace at towered airports. Even prior to September 16 1993, portions of "control zones" that extended beyond the basic circle around the associated airport were sometimes called "extensions", but this had no regulatory impact prior to September 1993-- these "extensions" were simply outlying portions of the "control zones". Prior to September 16 1993, communications requirements on VFR pilots at towered airports that were not "TRSAs" or "TCAs" were not associated with "control zone" boundaries, but rather with "Airport Traffic Areas", which were circles (5 miles in radius) around all towered airports (other than TRSAs and TCAs).
After the September 16 1993 "alphabet" airspace re-designation, "Airport Traffic Areas" were abolished, and VFR pilots were required to communicate with ATC before entering Class D (or higher) airspace. By designating outlying areas of control zones around airports with control towers as surface-level Class E "extensions" rather than as part of the Class D airspace, the airspace could continue to be protected as before, without imposing new communications burdens on VFR pilots.
Did the FAA originally intend these surface-level Class E "extensions" to be exempt from FARs that prior to September 16 1993 had simply applied to "control zones", and after September 16 1993 would contain language like "within the lateral boundaries of controlled airspace designated to the surface for an airport" or "within the lateral boundaries of the surface area(s) of Class B, Class C, Class D, or Class E airspace designated for an airport"? (This would include FAR 45.22(a)(3)(ii), FAR 65.37(f)(2), FAR 91.155(c) (formerly FAR 91.103(c)), FAR 91.155(d) (formerly FAR 91.105(d)), FAR 91.157(a) (formerly (FAR 91.107(a)) (later modified to present form), FAR 91.303(c) (formerly (FAR 91.71(c))), FAR 91.309(a)(4), FAR 101.33(a), FAR 103.17, FAR 121.347(a)(2), and FAR 135.205(b).)
The clearest relevant content we can find in the rule-making documents leading up to the September 16 1993 "alphabet" airspace re-designation is this passage from the May 1 1992 Proposed Rule "Terminal Airspace Reconfiguration", page 18956:
Therefore, these current rules for operations in control zones would
apply to operations in the Class E airspace areas that extend upward
from the surface..., but they would not apply to operations in Class
E airspace areas that extend upward from other than the surface.**
Unless the authors of this sentence simply neglected to address the status of the surface-level Class E "extensions"-- which seems unlikely, since the one of the primary purposes of this NPRM was to introduce the surface-level Class E "extensions"--the phrase "Class E airspace areas that extend upward from the surface" must have been intended to include the surface-level Class E "extensions" as well as the core Class E "Surface Areas" that actually surround and include the airports for which they are designated.
Therefore the sentence strongly implies that the FAA's intent was that FARs that formerly had applied to the entirety of Control Zones-- including any projecting portions, which even prior to 1993, were sometimes referred to as "extensions"-- would after September 16 1993 apply to surface-level Class E "extensions", not just to core Class E "Surface Areas" that actually surround and include the airports for which they are designated. If the May 1 1992 "Terminal Airspace Reconfiguration" NPRM or the August 27 1992 Final Rule "Terminal Airspace Reconfiguration" had intended to remove the surface-level Class E "extensions" from the scope of these FARs, that would surely have merited some discussion of the possible safety ramifications in the NPRM and Final Rule. (See for example FAR 101.33a!) No such discussion exists.1
It does seem unfortunate that the FAA didn't use the May 1 1992 "Terminal Airspace Reconfiguration" NPRM or the August 27 1992 "Terminal Airspace Reconfiguration" Final Rule to revise the proposed language of the FARs listed above to remove the confusing "designated for an airport" phrase. Note that this phrase had been introduced into the proposed language of these FARs in the October 18 1989 Proposed Rule "Airspace Reclassification" and the December 17 1991 Final Rule "Airspace Reclassification", both of which entirely predate any notion of surface-level Class E "extensions" to other surface-level controlled airspace. (At this time the FAA had planned other means of easing communications burdens on VFR pilots, such as making the Class D (and higher) surface-level airspace areas smaller than the original "control zones" wherever practical, and replacing outlying areas of "control zones" with "transition areas" with floors at 700' or 1200' AGL wherever practical.) Therefore the "designated for an airport" phrase was clearly not originally chosen for the purpose of excluding (E3/E4) surface-level Class E "extensions". It was simply intended to help distinguish Class E airspace that extends all the way down to the surface from Class E airspace that has a floor higher than the surface-- bearing in mind again that the selection of this phrasing entirely predates any mention of surface-level Class E "extensions" in any NPRM or Final Rule.
Note that any attempt to construe the phrase "designated for an airport" as excluding (E3/E4) surface-level Class E "extensions" causes problems with the interpretation of FAR 71.71(b), which also contains the phrase "designated for an airport": we would seem to be forced into concluding that (E3/E4) surface-level Class E "extensions" are not mentioned at all in FAR 71.71, and thus do not legally exist at all! This is undoubtedly not the actual intent of the FAA. FAR 71.71 is yet another FAR whose language was first proposed in the October 18 1989 Proposed Rule "Airspace Reclassification", and finalized in the December 17 1991 Final Rule "Airspace Reclassification"-- both of which entirely predate any notion of (E3/E4) surface-level Class E "extensions" to other surface-level controlled airspace. Clearly, when the (E3/E4) surface-level Class E "extensions" were finally introduced in the May 1 1992 "Terminal Airspace Reconfiguration" NPRM and the August 27 1992 "Terminal Airspace Reconfiguration" Final Rule, the significance of the "designated for an airport phrase" in the planned (effective September 16 1993) language for various FARs, including FAR 71.71(b), was a) simply overlooked, or b) judged not to exclude (E3/E4) surface-level Class E "extensions". The latter seems more likely.
It also seems unfortunate that when the FAA published the first (effective) edition of the "Airspace Designations and Reporting Points" document, FAA Order 7400.9A, on June 16 19932, the document was organized in such a way that the phrase "designated as a surface area for an airport" was only used to describe the core (E2) Class E "Surface Areas" that actually surround and include the airports for which they are designated. Surface-level Class E "extensions" (E3, E3a, and E4 airspaces) are placed in other sections of the document, and are described by the phrase "designated as an extension". The same structure and phrasing has been maintained in successive editions of the "Airspace Designations and Reporting Points" document all the way to the present day. In light of the fact that, as noted above, many FARs contain the phrase "designated for an airport", and most of these same FARs also contain the phrase "surface area", this choice of structure and phrasing for the "Airspace Designations and Reporting Points" document could be construed to signify that most or all of these FARs should not be considered to apply to the (E3/E4) surface-level Class E "extensions". And the FAA has in fact taken that position in some issuances from 2010 onwards-- for more, see the related ASE question this answer to the related ASE question "What indication has the FAA given that phrases like "surface area of Class E airspace designated for an airport" do or don't include E4 "extensions"?". But as described above, such an interpretation conflicts with the clear intent of the rule-making documents leading up to the September 16 1993 "alphabet" airspace re-designation, and also creates a problem with FAR 71.71(b).
In light of this, it seems that the FAA's choice of the language and structure for the first effective edition of the "Airspace Designations and Reporting Points" document, FAA Order 7400.9A, is best described as either a) an inappropriate rule-making action, unsupported by any actual NPRM or Final Rule, that deviated from the intent of the May 1 1992 "Terminal Airspace Reconfiguration" NPRM and the August 27 1992 "Terminal Airspace Reconfiguration" Final Rule and intentionally changed the meaning of numerous FARs by removing the (E3/E4) surface-level Class E "extensions" from the scope of these FARs, or b) sloppy authorship that was never actually intended to change the interpretation of any FAR or to remove the (E3/E4) surface-level Class E "extensions" from the scope of FARs containing language like "within the lateral boundaries of controlled airspace designated to the surface for an airport" or "within the lateral boundaries of the surface area(s) of ... Class E airspace designated for an airport". The latter interpretation seems the more likely one.3
Footnotes:
Note that such a change would have been a deviation from the intent of the earlier December 17 1991 Final Rule "Airspace Reclassification", pre-dating the concept of the surface-level Class E "extensions", which contains the sentences (p.65648) "However, the FAA desires to continue restrictions that currently exist in the FAR on operations within control zones." and (p.65650)"There will be no decrease in safety because there is no change in the type of airspace in which ultralights are permitted to fly or operate." Also note the extensive safety-related discussions in all four of the rule-making documents (NPRMS and Final Rules) referenced in the original question. It seems inconceivable that if the surface-level Class E "extensions" were intended to be exempted from FARs that had formerly applied to the entirety of "control zones", there would not have been explicit discussion of the safety ramifications of this in the May 1 1992 "Terminal Airspace Reconfiguration" NPRM or the August 27 1992 Final Rule "Terminal Airspace Reconfiguration"
The June 16 1993 edition of the "Airspace Designations and Reporting Points" document, FAR 7400.9A, was actually preceded by a previous edition, FAR 7400.9, entitled "Airspace Reclassification". This was issued November 11 1991 -- before the surface-level Class E "extensions" were conceived of -- and was slated to become effective September 16 1993. It was replaced by 7400.9A before it ever went into effect. It is organized slightly differently from 7400.9A, but it does contain (on page 9-132) the full text of FAR 71.71(b), as it read according to the version that at that time was slated to become effective 9-16-93. This includes the sentence "The airspace areas listed below are designated for an airport which consist of airspace extending upward from the surface to specified altitudes, within which all aircraft operations are subject to the operating rules specified in Part 91 in this chapter." (Italics added.) Then--bearing the title "Control Zones at airports without Air Traffic Control Towers", follows the list of all the surface-level Class E airspaces, all of which surround and include the airports for which they are designated. (I.e., all of which constitute what we now call "E2 airspace".) (Interestingly, in this version of the document, the phrase "surface area" is never used.) So the language of FAR 71.71(b) is actually the real reason that the phrase "designated for an airport" ever made it into FAA Orders 7400.9 and its successors in the first place. With this in mind, it's inherently problematic to cite the way the "Airport Designations and Reporting Points" document (FAA Order 7400.9A and later editions) uses the phrase "designated... for an airport" as evidence that surface-level Class E "extensions" do not fall within the scope of this phrase-- because, as noted above, the same argument must logically also be extended to conclude that surface-level Class E "extensions" have been entirely omitted from FAR 71.71(b), and thus do not actually exist at all. As noted above, this was surely not the FAA's actual intent.
It seems relevant to point out that, despite the problematic structure and phrasing of the "Airspace Designations and Reporting Points" document, each (E3/E4) surface-level Class E "extension" is in fact listed in association with the specific airport whose approaches it is designated to protect.
