The term of art is "missing middle housing".
The concentrated high-rise public housing model was an obvious failure and I don't think anybody is ever going to try to reproduce it. Ironically, where you see high-density high rise construction proposed (and resisted) most often now are luxury condo buildings.
Instead the existing (white) political machine used high rise public housing to explicitly punish and break up an ascendant black political block. They used highways and a university campus to the same effect.
In fill housing, at least in Chicago, is not a problem as we have both empty lots and tons of single family homes that can become 2 and 3 flats. Along with that you can add small specialized housing for various populations that need it.
Blueprint for disaster by hunt covers more specific policy and history of the Chicago Housing Authority