Mental healthcare is absolutely a salve for a lot of homeless folks. We used to have sanitariums and institutes - some of those were terribly abusive (seriously, they were horrific in some cases). Instead of fixing the abuse issues people found it easier to solve the problem by shutting down the evil institutions... then everyone who had been receiving treatment was forced onto the street and expected to take care of themselves.

Anecdotally, my wife (at the time a developmental psychologist) was commuting to SF from central valley every day because her pay wasn't enough to pay both rent and student loans.

In the end she left psych and went into tech. Problem solved!