Sorry, that's baloney. Mt kids get a far better education in private (parochial) school for HALF THE PRICE of what my local school district spends per student.
Monopolies (government or otherwise) ALWAYS deliver worse product at a higher price.
Because private schools get to pick their students. Public schools get all the kids kicked out of private schools for fighting, or using drugs, or not maintaining a sufficient GPA, etc., etc. Or turned away because the private school can't accommodate a student's disability...
Public schools have to take everyone.