Some people are essentially told to contribute to this phenomenon when you buy a house in the US. High home values mean good school funding, which means homes will hold their value over time, pricing out people of different incomes. Buy the cheapest house you can in the most expensive neighborhood you can afford for the best return (with the caveat that mixed use zoning is rare).
If had a Japanese zoning model,[0] decoupled school funding from local incomes,[1] and ended or capped the mortgage interest deduction, a lot of this would go away.
None of those are trivial changes without entrenched interests though.
[0] http://urbankchoze.blogspot.com/2014/04/japanese-zoning.html
[1] I've heard some states do this already. Oregon maybe? I know economic mobility varies a lot based on where you are in the US. http://www.npr.org/2014/01/23/265356290/study-upward-mobilit... Would be interesting to cross compare that with some of these policies, see how much they matter. Maybe the effects of redlining can't just be papered over so quickly.