Forget about "perfect". In a merely better system, "success in school" would be the last thing anyone thought about. The purpose of school is not to determine how well children navigate various arbitrary obstacles to learning. The purpose is to teach them, in whatever individual fashion best helps them to learn. If that doesn't happen it is a failure of the school, not of the child.

In a "perfect" system, the idea that anything about school would correlate with wealth would be viewed with deep suspicion. We're very far from that situation.

I interpret your point as "in a perfect system, school will be a playground, with no connection to a career, and everyone will have equal wealth."

I do agree that schools are culpable when a child (and parents) fails. I do not agree that we should take away the student's agency.

Did school teach you to over-interpret? I don't mention playgrounds, nor the "agency" of 6yos. Do you trust your 6yo's agency next to a busy highway? No? Then why is she responsible for dealing with her teacher's poor attitude and teaching habits?