You're absolutely correct - the average American theoretically believes that every child is entitled to a high quality, equal education, but in reality only if it doesn't cost them anything.

In light of that, there's very little that the state can do to force middle class families to stay in integrated school districts, and that issue destroyed integration efforts in the '70s and '80s in most of the northeast.

The real solution to the larger problem is probably a completely different education system, but the solution to this particular problem is to expand busing to the suburbs. If desegregation is the only solution to highly unequal educational outcomes, we simply need to pursue to greater lengths.