The public schools adopted the Prussian model after the civil war, which ipso facto, meant schools operated by the state. But public education, as originally under stood embraces the private schools as well, just as public heslth embraces all private medical facilities. Yes, the schools have socialized because the private schools are largely unable to compete financially.
Perhaps true in some areas, but where I grew up (south Louisiana), there was still plenty of local control in spite of the intrusion of the state government.
"Yes, the schools have socialized because the private schools are largely unable to compete financially.
That may at one time have been true, but given the exponentially increasing cost of public education is certainly no longer so. The USA spends more for (and gets less out of) "public education" than any other country.