Matthew Yglesias, in an New Jersey-apt analysis of one of the ways that traditional public schools "weed out" poor kids, notes that "one of the worst things about 'public' schools in many American jurisdictions is that even though the facilities are financed by the public they're de facto the private property of local homeowners:
In my view, over the long term the question of how linked schools are to particular places is a more important issue than the cliché debate over "charters" vs "traditional" public schools. In a zoning-free Yglesiastopia this might not be such a big deal. But in a real world where real estate markets are defined by location, location, location tying school access to location turns the school system into a form of private property. You can call a facility "public" all you like, but if the only way to gain access to it is to first buy your way into an expensive neighborhood then there's nothing public about it. It's just owned collectively by the residents of the neighborhood, in much the way that a luxury condo might have a fitness center or a gated community might have a golf course.