If a school-sucking alien mothership appears, we'll have plenty of other things to worry about. (Well, I won't, because Pat is the system lord, but the rest of you will.) Aside from that eventuality, the situation won't occur, so making predictions as to the outcome is pointless. In addition, I was positing the existence of privately funded schools, for those who wished to patronize them.
I think people are basically rational - even uneducated and/or not-very-smart people. If their incentives change, their behavior will change. If nobody supports adults sitting at home watching tv, they'll find something else to do or starve. If there's no "free" child care, they'll find some other way to avoid spending time with their children at home.
My observation is that avoiding time with their children is a very strong drive for many. The wailings of mothers on snow days or "teacher workdays" are simply deafening.
If a school-sucking alien mothership appears, I’ll be fine. My husband runs code for them, so he has a ‘deal.’ But it’s also nice to know I’ll have some company on the mother ship.