Parents are already paying a lot for improved education by moving to districts with decent public schools. They have to pay inflated housing prices because lots of parents want to move there to get their kids a decent education, and then they have to pay property taxes that go toward funding schools there.
Lots of parents would be happy to stay where they are and pay the cost of private education if it were available.
> magically get cheaper the moment you bring the "free market" into the discussion.
Capitalism isn't magic. It's incentives. Right now if a school is doing poorly there is almost zero incentive to change, because parents aren't legally allowed to send there kids to a different school out-of-district.