I've stayed in $30/night hostels in New York City. I don't see many places they could've cut costs and still provided a safe, sanitary place to sleep, and there are still homeless people in New York City.
$30/night is roughly $11000 a year, which is almost 3 times more than I pay in Pittsburgh for my share of a nice house. If there really is no way to cut those costs in NYC, the answer is to get out of NYC.
Just as Silicon Valley can be a good idea for a lean startup, Manhattan can be a good idea for the top tier of homeless person: The creativity, variety, and drive of the panhandling there is many levels above what you'll see elsewhere.
...I'm not sure where I was going with that, but even at $10/night that's the same you're paying in Pittsburgh.