My hospital has the hospital bed and a chair that folds out; there's nowhere for her to sleep. Plus there's no way I could relax and sleep because I'd be nervous about her running around and getting into things. I think she'd be more comfortable at home.
I know they can't make me stay, but if I've labored for 50 hours like I did with her and end up giving birth late at night I doubt I'd want to get everything together and drive right home, you know? And if you don't get a doctor to discharge you (which wouldn't surprise me if it's the middle of the night or something) then you have to leave AMA, which just doesn't seem like something that's that important to me.