>Schooling is generally expensive. Nothing compares to one-on-one attention from a skilled, experience teacher and that doesn't scale, so to have a better school, you really need to simply have more money to put into hiring more and better teachers.

Teaching is important, but I would argue that even more important are the goals and resources of the other students, which correlate nicely with wealth/income of their parents, and hence the neighborhood, and hence the school they all attend.

This is all barely noticeable when everyone is not so far apart on the wealth/income ladder, but over the past few decades, as that gets wider and wider, the data gets clearer and clearer about the consequences.