It does over time:
http://cityobservatory.org/what-filtering-can-and-cant-do/ or
http://cityobservatory.org/urban-myth-busting-new-rental-hou.... The problem is that we have a 40+ year backlog of underdevelopment:
https://jakeseliger.com/2015/12/27/why-did-cities-freeze-in-.... We've waited till the symptoms are acute to even begin acting on the underlying problems. Then we're surprised when we don't see immediate, instantaneous fixes.