One word: Mobility.
I lived in a slum in India and went to a private school that catered to poor kids. Got scholarship and worked my way up to start living into a high-rise. The private school had a big role to play in it.
That is not possible for low income neighbourhoods for USA anymore. The mindless regulations make private schools expensive. It is not possible for a retired school teacher to run a class-room in a garage at night and call it a school. That teacher will end up in jail and sex offenders registry. The poor hispanic neighbourhoods of south San Jose will have to rely on the pathetic public schools and those schools will ensure their students flip burgers. Those kids will find it hard to move to Palo Alto.
Public schools not only distort the housing markets but they feed into that evil spiral of poverty. I would love to see department of education dismantled completely and money given to kids to chose their schools of choice and let entrepreneurs make money by catering to the needs of all kids.