Right now you have good schools and bad schools and the way to get into the good schools is to have money and pay a lot for a house. The cost is more not because the good school actually costs more to operate, but because "having money" is being used as the admissions criteria, as a heuristic for not being a destructive influence.

It's pretending that public schools don't have any admissions criteria and then having one anyway. But because it's only that one, the market is broken. Dumb rich kids go to the good school and smart poor kids go to the bad school.

We could do the opposite. Give everyone a fixed amount of money for school, untethering the choice of school from your income, and then use anything else as the admissions criteria. Let the school choose its own. The schools with better-than-cheap-heuristic admissions criteria will be the most desirable, but will also accept desirable classmates regardless of parental income, because that's part of what makes it a desirable school.