[glhaynes]

Suppose we were to send in people to help everyone in the US to access all the educational opportunities that are available to them. This would still be a USA in which public schools are funded by regional property taxes — and thus a USA in which the schools in the poorest neighborhoods get a small fraction of the funding of the schools in the richest neighborhoods. Surely, then, average outcomes would still differ radically by region.

I think you've got a very good point at its core — people are heavily influenced by what they see around them; and, even keeping education expenditure distributed as-is, people can make a huge difference in others' lives by showing a good example and by passing on information on how to achieve in spite of circumstances. A limiting factor is lack of understanding on how to get ahead, yes — but, statistically, that seems likely to be only a small part of the story.