Children who attend socialist-entitlement and single-payer schools risk learning to be comfortable with socialism. Gee! If the local voting mob can give them tuition-free school, why not use the voting mob to get **lots** of “free” stuff.
Please remember. It only took one to three generations of single-payer and socialist-entitlment schooling to give the nation Woodrow Wilson and Franklin D. Roosevelt.
Secondly, maybe the starting point in each state would be the (assumed, implicit, but not stated anywhere that I know of) rule or law that all children must get a certain degree of education. The problem with a law like that is it has to be enforced. Assuming it's not a Constitutional law but a state law, then that means the state has to enforce it. I might vote to do away with such a state law and leave it up to the counties or cities.
My preference would be NO government law, leaving it up to parents to drive the free market and through voluntary demand and supply create the highest quality, lowest cost education we've ever seen. AND NO FORCED UNIONS. Sure, it would be difficult at first but freedom always is difficult at first. But it would lay a foundation for the best kind of educational situation anywhere and others would either flock to it or copy it.