Extended essay here that lays out how a number of districts, primarily in the south, where administrators have attempted to substitute income status for race.

One paper I haven’t seen by Sean Reardon, John T. Yun and Michal Kurlaender made a claim that’s certainly true for Philadelphia and most rustbelt cities:

“given the extent of residential racial segregation in the United States, it is unlikely that race-neutral income-integration policies will significantly reduce school racial segregation, although there is reason to believe that such policies are likely to have other beneficial effects on schooling.”

citation to track down later:
Implications of Income-Based School Assignment Policies for Racial School Segregation
Educational Evaluation and Policy Analysis, Vol. 28, No. 1, 49-75 (2006)