https://www.heraldsun.com.au/news/breaking-news/loose-link-f...
> Their results, released this week, reveal just over 30 per cent had a mental disorder.
> "The figure was much lower than the community perception and what other researchers had put out there," Dr Johnson told AAP.
> About 15 per cent had a mental illness before becoming homeless, while slightly more, 16 per cent, developed a disorder while on the street.
Sure, one study in one city, but assuming it's roughly correct, roughly half (if not more) of the homeless with mental illnesses developed them after living on the street.
So in addition to simply helping people not, you know, be homeless anymore, it would very likely reduce the amount of mental illnesses suffered by those who are and have been homeless.