I worked as a housing specialist for a bit (albeit in Columbus, OH. Not NY state) and the primary reason I would hear from landlords for not leasing a HCV tenant is either because of the limits on how much they can raise rent in a given lease period or they didn't like dealing with the housing authority itself. I have no experience with NYC's HA but if it's anything like Columbus, then it's a shit show for everyone involved.

On the other hand landlords are 95% of the time shit bags and slumlords. I almost got into a fight with one landlord because he refused to accept that the housing authority would not authorize his unit for inhabitance because it didn't pass inspection. In this case it was because he had an open outlet on the wall where water from a shower head would pour. Obviously not going to pass but he disagreed.