There might be some confusion over what "classical education" means. Do you mean a traditional/mainstream public school? Or classical as in structured around the trivium?
It wasn't clear to me, either - there's an education system conventionally called "classical education" and it is not what you refer to when you use that term.
I meant traditional public school, it's what I referred to as "classical" ("classical" in a sense what I believe most of us went through), though I understand there are private schools that in principle operate in similar way.