If we absolutely, positively "must" provide subsidized housing (not a legitimate government function in my opinion, but realistically we'll never get rid of it), the subsidies should be in the form of "housing stamps" or vouchers, allowing the beneficiaries to apply the vouchers toward privately developed rental units, or toward private mortgages.
Building new slums (government housing projects) is not the answer, no matter how "integrated" (in two senses of the word) they are with middle-income housing.
But, of course, it gets back to the plantation mentality, and recreating the political bases of Dem mayors, state legislators, and Congresscritters with creatively drawn districts.
I agree on vouchers. A related issue is that neighborhoods need a reasonable mix of income levels. This a more of an art than a science and I don't mean to suggest we need X of this, Y of that, and Z of something else on every block. But in a lot of places, Washington, D.C. for one, the poor get isolated because large swaths of the region are priced out of reach. You end up with the very poor dumped into de facto reservations with no jobs and very often with no very good way to get to a job across town if you don't have a car. So they sit, and trouble breeds.
Low income housing and social services providers need to be dispersed and decentralized. Every neighborhood should bear a part of the load. That includes the leafy suburbs.