The problem with public schools, and to a large extent with private schools today is that administrators and teachers are unable to distinguish philosophy from religion.
There are only three ways to think about reality. You can can a philosophic idealist (Plato, Lao Tzu) a philosophic realist (Aristotle, Confucius) or you can be a Sophist (De Sade, Heidegger)
Protestants and Greek Orthodox following Agustin early Church Fathers are typically philosophic idealist and this is reflected in their theology. Catholics follow Aquinas who was following Aristotle are typically philosophic realist. (Notice I am not advocating one over the other)
However, if you make an argument for ethics or morality from an idealist perspective in a school setting the idiots in charge call you a Baptist. If you try and make the argument as a philosophic realist you are denounced as a Catholic. Thus all that is left to the educator is the Sophistry that is Post Modernism.
While Idealism and Realism are different in many ways the ancients realized that the true enemy was was Sophistry and both were ways to combat it.
It is impossible to have any meaningful educational reform until educators understand this. Public schools should be, in their current incarnation be abolished because they teach Sophistry
Socialist-funded, single-payer, and compulsory schooling must be abolished because they can not be philosophically, religiously, culturally, or politically neutral. It is impossible for any sentient being to be in a state of such neutrality. It can't exist.
When government owns and runs schools, the most politically powerful will have the government ESTABLISH their anointed and NON-neutral worldview. The less powerful have their freedom of conscience and First Amendment human rights crushed.
It is a conundrum that has no resolution. IT CAN NOT BE FIXED!
Fundamentally...Government schools are a freedom of conscience and First Amendment abomination. That they are also failures academically is secondary to the crushing of the human spirit.
Some institutions must be shut down because they are, to their core, oppressive to the very nature of what it means to be human. They must be shut down even if those enslaved in the institution are worse off materially after emancipation. Slavery is one of these institutions. Government compelled incarceration in a government indoctrination camp is another.
In two tiny ways, the institution of slavery was actually better than government schooling. At least the government didn't force citizens to pay taxes to support it or force citizens to use or buy slaves. Also, in slavery, the whip was held in private hands. In government schooling it is the government police and government courts that do the punishing.