Bonus question-- why was the airspace portrayed differently on the VFR sectional charts in the first two examples (ACV and TVL) than in the last three examples (SGU, BIH, and SIT/PASI)?
After submitting an inquiry through an on-line portal, I recently spoke to a cartographer with the Aeronautical Information Services, who said in his opinion the depiction of the airspace at ACV was a mistake, and should instead resemble the airspace at SGU, BIH, and SIT/PASI. He is taking steps to make the change, and expects it to go into effect for the next edition following the 2-25-2021 edition. TVL presents a more complex case because the airspace description in J.O. 7400.11E does indicate that the E4 extension may not always be in effect 24/7, even though the present Chart Supplement does indicate that all the Class E airspace at this location is in effect 24/7. The cartographer indicated that he would take steps to see if there should be a change in how the airspace at TVL is depicted as well.
Was the FAA designing the airspace around these airports with an eye to minimizing the amount of airspace to which these FARs would be applicable, to lift the regulatory burden on certain aviation activities?
This seems unlikely.
Was the FAA designing the airspace around these airports with an eye to minimizing the amount of airspace to which these FARs would be applicable, to... limit the amount of airspace in which pilots would be eligible to be granted a Special VFR clearance?
This seems unlikely too. While it doesn't speak directly to the intent of the airspace designers, it is the case that in early 2019, I called the ARTC Centers controlling the E2 and E4 airspaces around these airports (except SIT/PASI which did not yet have E4 airspace at that time) and in every case the staffer I spoke to told me that in actual practice, they controlled both the E2 airspace and the E4 airspace. The staffers also told me that they makemade no distinction between E2 and E4 airspace at these locations in terms of granting a SVFR clearance.
What is the primary reason that the (U.S.) non-towered airports ACV, TVL, SGU, BIH, and SIT/PASI all feature E4 Class-E-to-surface "extensions" to the E2 Class-E-to-surface airspace that surrounds the airports?
Why was the airspace not simply all designated as E2 Class-E-to-surface airspace, as was done at SHR?
This answer is unable to address those aspects of the question at this time; it remains unknown.
But, regardless of the reason, it is a positive thing for those flying small Unmanned Aircraft under Part 107 or the 2018 "Recreational Exception", and arguably for ultralight and aerobatic fliers as well. For more, see this related ASE answer.