The way Denmark and Sweden tackle the problem very successfully shows that combating homelessness is largely an issue of the right social policies: https://en.wikipedia.org/wiki/Homelessness_in_Finland And it actually saves money too

Sure, simply providing housing may not solve everything, and complex measures must be taken to ensure mental wellbeing, fiscal responsibility, lack of addictions etc.

But housing and income must come first, as not having that prevents effective therapy. When you're in survival mode, you're not particularly productive resolving your other issues.