>>monkno+(OP)
+1. That being said, universal k-12 schooling works because it is publicly run. A subsidized private sector model has a lot of bad incentives and issues to work out. As an example, I've sent my kids to a private school for the past five years, and last year our state introduced a voucher program to help subsidize private education. The school responded by raising the prices by almost the amount of the voucher, just for the age groups that it covered.
See also: US healthcare.