The problem with government schools is far more than mediocrity, although you are right about this.
Let's change the language regarding government schools. Government schools are an offense to freedom of conscience and that makes them human rights abusers. Since children are involved, government schools are child abusers. This far more damning that pointing out that their service is mediocre.
If the only argument against government schools is mediocrity, then others can suggest that we improve the quality of government schools. No. No. No. Government schools must be eliminated because they offend basic human rights to freedom of speech, freedom of press, freedom of assembly, and government schools establish the worldview of some citizens ( with religious consequences) and undermine the most closely held family traditions and beliefs of others.
The following is what should be said about government schools:
Government schools are human rights abusers and child abusers!
Government schools use the threat of police force ( real bullets in those guns) to force children into buildings where they are stripped of their human rights. They are indoctrinated by the government in a worldview that has non-neutral political, cultural, and religious consequences.
Why is it impossible for government education of the young to be neutral in its content or consequences? Why is this so? It is because time and resources are finite. Government schools must choose what to study in depth in its curriculum, what must be superficially covered, and just what topics will be completely ignored. In making these choices the government school will favor the worldview ( with religious consequences) of some of its citizens and undermine and even sabotage the worldview of others.
The truly offensive quality of government schools is its power to use police, court, and foster care threats to impose its will on American parents. Since government schools ( being price-fixed) have created a business climate hostile to private schools, often making it the only option open to parents.
Government schools use the threat of sheriff's auction of homes and business to fund this abuse.
This is the language that must be brought to bear against government schooling. It is like Reagan when he called the Soviets the Evil Empire. From then on, the Soviets had to explain why they were not evil.
It is time that government school defenders explain to the rest of us why government schools are not evil human rights and child abusers. Of course they can't and it is this that will bring down the government schools.
Because humans by nature are not neutral. Neither are scientists. Of all the educational endeavors that have an effect on one's world view, the so-called natural sciences are it. Hence it is no surprise the debate between theistic and non-theistic principles is a heated one. Non-theistic principles are not neutral, either morally or scientifically.
Many scientific disciplines, and much education, may carry on without invoking either one, but when they do, it is incumbent upon the educator openly to admit as much. As it is, the larger part of evolutionism in public schools is non-theistic philosophy foisted by stealth upon a captive audience in the name of science. The old canard that organized matter and purpose can only be understood as a religious concept seems to have been swallowed whole cloth by we the people who pay for public education, along with the old canard of "wall of separation."
I share your view that public schools are a disgraceful abuse of the human mind, not to mention physical resources. Vouchers would be a good way for those intellectually superior atheists to start and support their own schools without all that superstitious psychobabble dragging them down and, as a result, get all those super high paying jobs, like head curator at the Smithsonian Museum of Natural History.