“To become a fine thinker requires substantial schooling, typically home schooling.”
I think you are wrong about this. The classical education you so highly praise points to Socrates (Socratic dialogues) but Socrates never went to school. He, apparently, was a brick layer who was accepted by the Athenian aristocracy on his abilities to think. If anything he was self educated by his natural curiosity on subjects ranging from science (early Socrates) to virtue (later Socrates).
But, for the most part, Socrates is the exception and not the rule. The value of a classical education is to assess bias in an unbiased way and that, for me, is a far better way to go than viewing everything through the same Marxist lens of grievance and social justice.
Disagreement on this topic can best be laid at the feet of socialist public education. the very notion that one can not learn to think critically is the product of unthinking and uncritical mass socialization.
The struggle to become more is the essence of an educated person.