I wouldn't want to go to an all private pay system, that would leave children without means out of luck. I do think there is a role for private schools, I went to one myself for high school and was very happy with the experience.

Anyway, there are a variety of different ways we could imagine loosing the tight coupling between housing and schooling. I mention downthread that I think school choice / vouchers is a promising approach, but I am open to other ideas as well.