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.
I’m in a rent stabilized studio unit in Manhattan, and my rent has gone from $1125 to nearly $1700 in the dozen years I’ve been here; I’m now hard pressed to budget it, and I can’t afford to move anywhere remotely nearby.. My income hasn’t risen proportionally, as this report suggests is often the case. The rent guidelines board has hiked rents considerably every year, and we low-to-mid income renters desperately need a break. Please keep your campaign promise, Mayor De Blasio, and FREEZE stabilized rents at their current levels for a while.