Because moving to NYC from pretty much anywhere else would increase your annual cost of living by far more than $5,000. Net you’d lose.
I'm progressive but I recognize the issues with municipal universal welfare.
So unless they set up some kind of residency requirement or collect biometric info from the homeless and register them as NYC beneficiaries, I don't know what would keep homeless people from coming from other areas (other than, of course, a lack of money or transport).
I am genuinely unsure.