This is anecdotal evidence gleaned from various forum and reddit comments, but I think it makes enough sense that I can justify making it an answer.
FAA Air Route Traffic Control Center (ARTCC) sectors are identified by a name and a number, or only a number. Boston Center, for example, publishes a sector map in a Letter to Airmen; a Syracuse Approach controller trying to contact the Boston Center controller working the "HNK23" sector might say either "Hancock, Syracuse, apreq" or "Two-Three, Syracuse, apreq." The TRACON systems and the ARTCC systems both keep track of ARTCC sectors by assigning each sector a one-letter two-number code, like
C23 for "Center, sector 23."
Back when standalone TRACONs first came online, the ARTCC automation system (which may have been HOST or may have been an even earlier system) did not have any possible designation for a sector besides
XNN. This is important, because the system needs to know who exactly should be on the receiving end of an automated handoff (where the identification of a radar target is transferred from one controller to another via computer connections, instead of the controllers verbally discussing the location of the target). So the new facilities were added to the center systems as if they were just another sector at an external ARTCC, using the same designator format. By the time facilities like PCT, NCT, and SCT came into existence, the systems had been upgraded and no longer required the workaround.
...Of course this doesn't explain how the system would deal with a normal non-separated TRACON like SYR, so perhaps this answer isn't correct after all. But I have seen it a couple of different places.