Just HOW do you propose to do that politically?
Then...As some children on the block go to private school, the other parents begin to say, “Hey! How come **that** kid gets a tax credit to go to a local, safe, and effective private school and my kid doesn't?
Or....Offer a very very very few vouchers, then have parents line up by the hundreds in lines circling the block as the await the annual lottery pick. Be sure to show plenty of Youtubes of kids and parents crying because they didn't win.
Do that and political power for chance will build.
Do I think vouchers or tax credits are the best? No, I don't but they can be a means to break up the government school price-fixed monopoly and build a private infrastructure. Gradually, parents should be expected to pay for schooling. Gee! It's amazing how parents can pay for daycare but once a kid is 5 they insist on government babysitting ( oops! “schooling”).
The best of all worlds would be complete separation of school and state.