The reason NYC didn't tear down it's high rise projects as other cities have done is due to the fact that 1. There is no private sector "low rent" category in NYC, even in the Bronx, 2. Only a few landlords in far out neighborhoods (ie Canarsie, Baychester) accept Section 8, as they can usually charge more in the private market than what the government offers 3. In NYC, 35-40% of project dwellers are "chonics" ie spend their lifetime on the dole, as opposed to 90%(!) among Chicago project dwellers. and 4. Many of the folks who live in the projects are elderly, don't want to move, and VOTE.
NYC is the only place I can think of in the US where you have people paying $3,000K plus a month for a studio two blocks away from the projects (see the west 100s, the Lincoln Center area, Chelsea, etc.). If said folks were to be relocated to "low rent" areas, it would have to be in Pennsylvania or Troy.