Where do you claim there are favorable conditions? As far as I am aware the homeless are everywhere; some places are simply impossible to live without shelter due to exposure.
Housing affordability and degree of government involvement are both on a spectrum; you don't need extremes to see if there is a relationship or which way it runs.
Affordable housing is code for unaffordable housing. Otherwise it'd just be housing. You're very correct it's on a spectrum—we're between being entirely homeless and entirely housed. Only one end of that spectrum is acceptable. Housing should be free to use (obviously not free to build and maintain). Everyone needs it, and we all have incentive to reduce costs—except landlords.
Right, so the market is what makes housing unaffordable. Making housing a guaranteed human right will make it entirely affordable—at least on the end of using it. Housing is entirely a cost that should be amortized over those able to afford and/or build it.
In socialist countries. In the Soviet Union, rent was 2% of take home pay. Many of these countries started out poor, so the housing quality may have been commeasurate with the development of the country. In the US, as a material issue, we could easily provide decent affordable housing to everyone by destroying the market and having the public march in and build.
One system that is being tried in some region in China is you buy your house from the government and sell it back. This keeps things democratic and market free. Landlords should be cast into the dustbin of history.
We have, I believe, about 3x the empty units as we have homeless people in this country. Sure there are distribution issues, but it’s a matter of political will.
Political will to redistribute the people? You must know that that's how it worked/works in socialist countries. You still need a permit in China to move to another city, AFAIK.