Why not a free market in education?
Parents pick the winners and losers, and the best schools rise to the top, while failing schools are filtered out. Parents measure quality by whatever metrics they find to be the most useful and reliable, just like with any other industry.
Competition forces education firms to constantly outperform each other in a race to maximize utility, meaning a race in providing the most useful and valuable education, at the least cost to parents. And new innovations, efficiencies, and ways of operating and providing education are discovered along the way that likely wouldn't have been discovered with a nationalized government-run school system.
Pair this with a government subsidy for lower-income families, so they can also afford to send their kids to great schools, and what is the issue?