I imagine there will be some characters you'll be able to recruit in different houses - i.e., you can pick which house to send to do a paralogue that unlocks someone. I'd peg that as the exception to the rule though.
Also, I'm expecting at least 20 "WHICH THREE HOUSES HOUSE ARE YOU?!?" Buzzfeed-style quizzes from fans who want to sort themselves and their friends.
(Side-Note: There is an officially-sponsored
"Which P5 character are you?" quiz to promote Dancing in Starlight. I'm Haru.)
That is true. If it happened, I imagine it would be the singular enhancement being made for the game. It would also require quite a bit of rewriting, but I also imagine the rewriting would be a bit easier then P3 in a sense? Like, it's very obvious how a female being a figurehead of a group of societal rebels would be transgressive ,though I also recognize that the amount of rewriting may make it not worth doing nonetheless. I don't know how popular the FeMC was in Japan - obviously she was in PQ2 and they wrote the musical adaptation of Persona 3 twice for each protagonist (yes, that exists and is worth a google if you enjoy weird dance-fighting to the P3 OST), but her not being in P3DMN is... weird.