Pretty much nobody in my friend group (and we're all parents) would prefer to be a stay at home parent. Personally, that's a bad fit for me, my skill sets, and my preferences. I'd be miserable and bored, and feel that it would be a waste of the things I'm good at. My wife would feel the same way in that kind of caretaker role.
Like, I think if we won the lottery and didn't have to work to maintain our lifestyles, we'd still send our kids to school and camps and things like that to get them out of the house and socializing with other people, while we'd probably still choose to work in some capacity, for some kind of public interest or passion project we'd do for reasons other than the money.
Staying at home with kids just doesn't sound appealing as a day to day routine. I like my weekends with them, but I also like that we use the time to catch up, too.