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I agree this is probably the biggest tradeoff, but attention all parents, there's a cunning and affordable solution to the challenge of spoiling versus opportunity. It's guaranteed to work, anecdotally, at least sometimes:
Live in a big house and send your kids to a nice school, but roster them on truly hood (n.b. I mean real deal heart of the ghetto) travel sports teams. Only two requirements are as follows:
(1) that the team must be decently coached and
(2) practice field and home field must be in a genuinely scary neighborhood. Please don't assume I mean a run-of-the-mill bad neighborhood.
Ideally Pop Warner when younger and AAU BB by high school, but really anything other than lacrosse or fencing works. I personally was raised on hood travel baseball, and I am being 80% serious about this suggestion. Go Hurricanes.