I lived in Cambridge, MA, and they have successfully desegregated their schools with a similar approach that kept transportation very low and remained a popular plan with most parents (75% approval income over $100k, ~95% approval income under $75k).
In another place I lived, the top public magnet school was ~95% black. White parents pretty much universally refused to send their kids there, but would send their kids to a different magnet that was further away.
The "underlying socioeconomic realities" are often overstated compared to the unfortunate, but big reason that we don't like to talk about, which is lots of parents (to some extent, understandably) are afraid to send their kids to a school where they would be in the racial minority.
Schools are now as segregated as they were in 1976, which represents a backtracking from the peak in 1988. That represents an erosion of will more than a vastly changed socioeconomic reality.
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.