Yeah, Hazel specifically says she's stuck in the apartment now with even her description at stage 10 saying as much, but then she goes about her normal business throughout the city. I'm a sucker for immobility so I would advocate adding it in even if it's a one-girl-per-game kind of thing. It could also be used to unlock their rooms for you to freely enter since they're permanently stuck there, and each one would have a different kind of immobility (the one with a giant chest could have breasts so big she can't leave the apartment anymore, for example).