As insulting and socially destructive as that is, this whole discussion does not do justice to the housing challenges of New York City's poor. The "affordable" units in the new buildings are still positioned at incomes around the city's median household income. This is not housing that is within reach of the poor. This fact provides some support to the push back against the critics of this practice; many people just aren't that sympathetic to the insult to residents who could afford a typical apartment but have won the opportunity to move into a much nicer unit because they happened to win a lottery.
This situation is typical of the public discourse around affordable housing in New York City. There is attention and programs for the middle-class, with public debates back and forth about how much support professional workers really need and deserve. Meanwhile, the units that are inhabited by the working poor, who spend so much of their earnings to inhabit apartments with much worse conditions than new construction with a side entrance, are places that remain invisible to public discourse.
The poor have always inhabited the residual spaces of the middle class. Sometimes these were neighborhoods of speculative middle-class housing that were left over from a glut of housing bubble, ultimately becoming crowded ghettos as the houses were chopped up into apartments. Other times, and increasingly in New York City today, it is extra space in one- and two-family houses in neighborhoods where the working class moved in after the original middle-class owners moved on. These less affluent owners often can no longer afford the entire space for themselves as they struggle to pay the mortgage and maintenance on the structure. Many turn to renting out rooms for supplemental income. These are the illegal apartments that fill basements and cellars, and dangerously partition floors in houses throughout the city's sprawling residential districts.