I believe we have confused the term “public education” with “government schools.” Public education is not necessarily government education. It has just become that by government takeover.
Public education was created in the 1600s by the Puritans. It predates this country. Indeed it helped create the New England common people who were educated and independent enough to start the revolution that created our country!
For the first 250-300 years public education was NOT government education. It was a publicly held, locally owned corporation where the local property owners (taxpayers) were the shareholders. They controlled education. This changed when, first the school districts in growing cities became big. They became the flag ships that everyone looked to. Their property values (and thus tax revenues) increased rapidly, while the rural, smaller districts did not. The smaller districts coveted the revenues and begged for state revenue sharing. That led to state control, which might not be so bad, but that led in the 1960 Presidential election to Kennedy blaming schools for Soviet space advances and at the same time promising federal funding for them. That is what won the election for him, and THAT is when the change to becoming government schools started. False philosophies had been around for 50 years and more. They had some limited impact, but did not prevail until the national takeover began.
Public education isn’t the villain. The villain is government intrusion, which has been bought with tax revenue. Even the union isn’t the fault. It is rather an indication and complicator of the problem. The cancerous philosophy that government can guarantee success has grown exponentially in the last 50 years. It is destroying self responsibility and initiative. It also promotes and protects false philosophies. Actually it is amazing how good the schools are given the situation. That is a reflection of parents and teachers who have held to correct beliefs they grew up with and learned in their families and churches. Otherwise the schools would be much worse, and are in some places.
A community coming together to do the education of their children is not the problem. The problem is national interference and take over. Eliminate that, including restoring districts to community size, and education would be more likely to do a better job.