IIRC New York City actually has higher rates of housing/sheltering homeless than most other cities in the USA. However, due to population size + density it would still be possible to see the homeless people who refuse/cannot access housing fairly regularly if one lives in or commutes to the densest areas. (For example, I've only ever seen homeless people in the heart of manhattan. I commute to Astoria and Flushing and long island fairly often and hardly ever/never see homeless people there.)
