Somehow, though I see your logic, I doubt that that would happen in practice. Rents would remain stable and continue to climb, I think. Landlords will demand as much as they can possibly get, and in Manhattan (south of Harlem, anyway) they will find takers. I think what you suggest would likely only hasten the exclusion of low to mid income earners to the far fringes of the other boros, while the well-to-do and super rich complete their take-over of all the desirable/convenient neigborhoods. Diversity and cultural interest will suffer, as the core city becomes ever more homogenous.