Some of the smartest, truly well educated people I've met started from one room country schools of the early/mid 1900's. Granted, they were 'public', in the sense that a group of neighbors got together, built a schoolhouse, and hired a teacher. -- But they were a far cry from the institutions we have now. - And the kids are the worse for it.
In those days, only larger communities had high schools, [many of which were private] and again, the smaller the school, the better educated the children, imo.
The state run, consolidated public school system is an observable failure.
There are many outstanding people educated by the public schools throughout our nation's history.
Most of the attackers of public schools simply don't know what they are talking about. Millions of children are educated every year successfully by them.
Could they be better? Sure. We should strive to make them better not wholesale lies and misconceptions about them. Or pretend there is a private alternative for the masses. There isn't.