People think mental health causes homelessness, but it looks increasingly like it's the other way around -- cities with bad housing crises and insufficient shelter systems (NYC is notable for having an excellent shelter system compared to its peers) end up with people who hit rock bottom and become destructive out on the street when they'd be trying to get their lives together if they had a place to live.
If people can't grapple with their demons in the privacy of their own homes, they will grapple with them on the subway and we'll all be collateral damage.