America's top schools are privately-run (Harvard, MIT, Stanford, Andover, Exeter, etc). If we eliminated private schools, does the author expect better test scores?
The use of "school" here is about primary and secondary education, not University/College level tertiary education.
So? My point still stands. The best secondary schools, like Andover, Exeter, Harvard-Westlake, St. Paul's, Horace Mann, to name a few, are privately-run.
I wasn't disagreeing with your point, merely pointing out that in this context those were poor examples.