While I share your perception of it being a nuisance in public spaces (try to find a seating option in Grand central...), limiting access won't resolve the issue.

NYC/NY/US needs to invest in social structures. As long as there is unnecessary/artifical poverty created by inhumane conditions, bad social structure and economic exploitation there will be homeless people. With the current developments in environment and society, if you're not making at 100k, prepare to become part of the issue over the next two decades.

Excluding them won't stop the issue. The US wishes to be #1, but really often shows they aren't, by far. Below the poverty line bo not live lesser people, just the less fortunate one's.