After much digging around, my working theory is that it allows vessels controlled exclusively by non-pilot kerbals to upgrade from "limited crew control" to "full crew control," allowing you to create maneuver nodes. You'll still need a local source of SAS in order to not hate your life, though, so you're probably bringing along a pilot or probe core anyway (not to mention an external antenna, if you're going beyond LKO, or transmitting science). This is evidently what the enigmatic "Remote Pilot Assist" feature refers to when it appears in command modules that require crew. Incredibly obscure!
(I feel sort of awkward for answering my own question, but then again I did wonder about this for days before posting, and I only just now thought up something that I could test...)
PocketBrotector's post in What's the point of the internal antennas included in command pods? was marked as the answer