Remember, this is in comparison to public schools, which are regional gerrymandered monopolies. This system isn't perfect, but sets incentives in place to make it better. I grew up near some sketchy neighborhoods, and although I went to an average school, I know a lot of people who fared worse.

I'm not going to write a response to everything you said, but the tl;dr falls into a few categories

1. Privatization does not mean deregulation. Imagine Obamacare style regulations to a private marketplace for schooling (price caps, cannot turn away certain sets of people, etc).

2. If we can't agree on some measure for effective education, then there's no way to improve this, since we have no bar to go by. Everything is empirical and mileage may vary from person to person. You can create a seperate class of high school education (will flesh out in next point).

3. Property values are strongly correlated with the quality of the public schools (since all states help pay for public school with property taxes[1], and you are locked into a public school depending on where you live). My main motivation for supporting this is to help poor people have access to the same quality education as everybody else, and maybe even allowing specialized tracks that bias towards vocational schooling that funnels into direct employment after school (universities can boast about employment post graduation, why not high schools?)

4. There is nuance with the specific numbers here, and if it is systemically impossible for reasonable competition, then this price will go up.

[1]: http://www.ncsl.org/research/education/funding-approaches-th...