> there are plenty of places (like my hometown) where parents send their kids further out to ensure that they attend a school that is majority their race rather than the local neighborhood school.

Ah, that is interesting. In my district (and state, AFAIK), school assignment is completely out of the hands of the parents, with some narrow exceptions.

I fully admit to having a narrow view on this, my state is not especially diverse, with more than 75% white and 2% black. So most of our school segregation, if it's fair to call it that, is completely socioeconomic even if the students are largely the same race.