Idk about NYC but the people I see on fent in west coast cities’ homeless encampments couldn’t pay a $500 rent any more than they can the $5,000. They’re strung out all day long and can’t pursue any goal besides getting more drugs.
On the other hand though, a lot of who’s technically homeless at any given time aren’t that chronic, mostly hopeless, and very visible set. It’s people who did lose their apartment just barely after an unexpected job loss or medical expense. Those ones could be helped by cheaper rent! But that group isn’t very visible, doesn’t bother anyone, and often couch surfs, sleeps in their car and showers at the gym for a couple months, etc. and most importantly, they use the many safety net resources to get back on their feet (getting a job usually).