The free market has no incentive to solve the problem. Charity is nice but has limits in terms of scale. The government is the only entity that could feasibly implement a housing guarantee or something close to that.
Charity is a free market component. A person willingly chooses to donate time/money/effort to a specific group they like directly. If the government were to do it it would be person -> taxes -> different levels of government -> gov program. As you can imagine resources are burned up through the levels and because every party is so far removed from each other they don’t act with proper ownership. Nor do they care.
Let me quote you from one of your other responses: "My help comes in the form of taxes I pay. I'm willing to pay more if it means people get housed."
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".
> 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.
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.
> The free market has no incentive to solve the problem
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.
You asserted "the free market has no incentive to solve the problem." I responded with a counterfactual. The broader assertion, that the free market will solve the problem, was not made until now. I agree with you on that.
Affordable housing is not a hard problem to solve, unless local government dirven by NIMBYs, places roadblocks on developers and high density housing development.