Your point makes sense in regard to welfare, although to be honest I don't really know anything about it so take my agreement for what it's worth.

I agree school segregation is a self reinforcing loop, because school segregation is both a cause and an effect of income inequality (via geographic segregation). But we could short that circuit if there were the political will to put resources into creating incentives for local governments (it's very expensive), teachers and parents. In the FY2017 Obama budget proposal, there was originally a $120 million grant program for integration, which was eventually reduced by 90% to $12 million. Now Devos might cut that in the name of "school choice" -- a dog whistle for de facto segregation.

On the other hand, if we choose to follow political decisions (in this case, politically motivated legal decisions) like Miliken v Bradley and allow de facto segregation in schools, then we will never be able to have the equality of opportunity that would narrow the income and achievement gaps across races and prevent auto-segregation.

Another thing to consider is why we can't appreciate the inherit incentives of school integration: It appears to do a whole lot of good for a lot of kids. Integration leads to higher achievement in several subjects, especially for black students. Based on the research I've seen, there is little to no effect on white students' performance. I don't know of any other pro-equality public policies that minimizes loses as much as integration does. As for the big picture, the potential knock-on effects of reducing systemic inequality should provide a lot of long-term incentive for white communities to embrace integration. It's not a panacea, but there are a lot of reasons to be (cautiously) optimistic about school integration.

I think one, maybe not the only but at least one, reason we don't think about the inherit incentives of integration is that racism makes supporting integration politically toxic. Both white and black communities were widely opposed to integration in the 70s, and white families fought particularly hard to keep black students out of white schools. After that, white flight kicked in to avoid having to send white kids to predominately black schools.