Of course, short of the Democrats controlling both houses of Congress and the presidency, that seems rather unlikely to happen (and even then it's far from guaranteed). Certainly the GOP doesn't seem very concerned about this issue.
Now, what could help is relaxing zoning enough to build more housing, thus making housing itself cheaper. With cheaper housing, something like Salt Lake City's Housing First program would become more feasible.
But that would probably require ending Seattle's USA-standard segregationist zoning to allow more density in more of the city, and doing that is fraught with peril, politically. People are used to the government enforcing a certain lifestyle in their neighborhoods, and don't like the idea of the market letting in more people, especially people considered 'undesirables'.
[1] https://www.nejm.org/doi/full/10.1056/NEJMp1710756
[2] https://www.addictions.com/opiate/the-role-of-pharmaceutical...
My New York City neighborhood's commercial association felt incentivized to solve the problem. It finances outreach, education and relocation (to shelters) efforts to keep the neighborhood pleasant. In any case, a large part of the problem is created through voters enacting silly housing restrictions.
The free market certainly does some good, but it's never gonna solve the problem in full. If it could, it already would have.
If charity could solve the problem, it already would've.
If you're willing to pay more above the taxes and do so, you're already part of the solution and you're already performing charity without the need of government.
If you convince enough other people to do the same, then you're good to go and you'll have enough funding to solve the problem. Unfortunately, as with everything government, you actually want/need to use it as a big stick for more taxes or for tighter regulations when people don't behave the way they're "supposed to".
No. I'm willing to pay a large amount to go towards public housing as taxes, but not as charity. The distinction here is that it coming in the form of taxes ensures that everyone (or at least everyone able) is also paying their fair share, and that we'll have enough for a substantive impact.
I don't have much interest in putting in extra while homo economicus types get the same benefits of living in a society with fewer people homeless while not contributing.
If you have a solution that's been more effective than government social welfare, public housing and saner zoning in, say, Western Europe, I'd love to read about it.