In NYC units that might be _actually cheap_, as in rent controlled and not stabilized, number roughly 17k units _in total_. And only about 1/3 of those are significantly below market or in desirable neighborhoods. It's almost insignificant and the number of rent controlled units has gone down by roughly HALF in the last 5 years, because the tenants in them are dying and income limits on any descendants usually kick the units out of being controlled into stabilized.
NYC has a much larger number of rent stabilized units, which is somewhere near 1/3 of all available units that are renting at or below $2700 (twice the national average, btw). The overwhelming majority of these are within a few hundred dollars of market rate.
There are about 4.2M housing units in NYC with roughly 30k being added every year. The "cheap" rent-controlled units are a rounding error.
That is not anything like the situation folks in SF are rightfully railing against.