Keep the public schools closed permanently.
Give parents a refundable tax credit in an amount sufficient to send their daughters and sons to excellent private schools.
That would cost less and result in actual learning.
One of the reasons I read for not allowing private schools was because they could reject discipline problem children and they would suck away the better students. Public schools would then be forced to take the problem children and would have only the slow learner students. We would end up with a two tiered education system. Instead, public schools turn out a uniformly bad product.
Subsidize private schools to that extent and then they become public schools in everything but name. If the government foots the bill then they get to say how they're run.
Or to use for homeschool materials
Give parents a refundable tax credit in an amount sufficient to send their daughters and sons to excellent private schools.
The only refund they are entitled to is the portion of property tax paid to fund the schools. From my experience, that is insufficient to pay for an “excellent private school”