So if we look at places in the US with more favorable housing conditions, we should find housing allocation done primarily by the state?

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.

>Only one end of that spectrum is acceptable

Which makes it all the more important that you correctly identify and apply the mechanisms that push a place towards one end or the other.

>Everyone needs it, and we all have incentive to reduce costs—except landlords.

64% of housing units are owner-occupied [0]. These households are not landlords, yet they are incentivized to raise property values.

[0] https://www.census.gov/quickfacts/fact/table/US/VET605217

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.