If classrooms are not conducive to learning, why do private schools do so well?
They don't. They are all subject to control by government in some degree, so their success is marginal; they do better because parents can
influence them strongly (they can remove children and the fees paid, at will) and because they are well
managed on a business basis so can afford to pick high quality teachers.
Some get close to the ideal of 1:1 learning by providing teacher help only upon demand by the child. One such is Sudbury Valley School in Massachussetts.
When parents pay directly, they make
very sure that Junior takes full advantage of the teaching offered; so the home influence is very strong.
The reality is that their tuition is little
better than that in government schools but they have a well developed "old boy network" that ensures career success after graduation regardless of real performance.