> A situation like this where the salary doesn't really depend on location so it wouldn't be treated like I'm actively trying to game anything would actually be preferred in my situation, and to many others I know as well.

Exactly. We've had multiple employees move to different cities/states during their tenure. That wasn't a problem with us (from an employer perspective) and there was also no expectation that salary would be adjusted in response to a move, since location wasn't factored into the original offer in the first place.