The good school / good neighborhood thing is a self-reinforcing cycle. Wealthy families move to neighborhoods with better schools, increasing local tax revenue, which gets invested into better and better schools, which attracts even more wealthy families. On the other hand, middle class flight leaves poor families in shitty districts, reducing tax revenue, which means worse and worse schools, which means more middle class flight. The incentives guarantee this will happen.

We need to separate school funding/quality from neighborhood affluence but that's a tall order politically.