I think you know a lot about Japan, so feel free to correct me, but I wonder if that system works so well in Japan primarily because of the culture
Well yeah, here is not there. The thing about Japan is that it's full of Japanese people. They also have regular old fashioned homeless people in Japan. They are under most bridges in central Tokyo. But there is also a large contingent of people, who knows if it's thousands or millions, who are functionally homeless, but because they are able to scrape together living resources they are actually *functioning* homeless and still manage to have a job. If the environment were more hostile to the poor, there would be much higher numbers of regular-homeless.
I think in America we assume all homeless are mental or drug addicts. A lot are. But as the economy worsens there will be a larger contingent of people who are homeless just because they are homeless. Between minimum wage laws, degree inflation, skyrocketing housing costs, no cheap housing construction allowed, can't get a job with an arrest record, absent or unreliable transportation, etc. etc. there's going to be a larger number of people who could be more functional, but we aren't making the environment easy for them to be.
To me it's a very American thing to have a lot of rungs on the lower bit of the ladder so people have every opportunity to better themselves if they can. Then you will still have a homeless problem but hopefully the bare minimum. That's not necessarily what I see. Instead I see more that America is a good place to live if you are (relatively, by world standards) rich. But not a good place if you are poor. And I don't like policies that remove mobility and opportunity for poor people, especially if people think they are helping the poor people situation by doing it.
A central question is whether the government should spend money on helping the poor at all, or just laisse-faire. However currently laisse-faire is a joke already in America. Can't build any cheap housing, because we don't want slums. Can't provide credit to those who need it most, because exploitation. Can't hire people for what the market will bear because minimum wage. Can't even have cheap cars because of safety standards. What I see is active policies that remove the lower rungs of the ladder without replacing them with anything. If you look at Europe policies, they are more welfare-y. I don't necessarily want a welfare state but, maybe like how you can't have a welfare state and open borders, maybe you can't have a bunch of policies like this without also throwing money into welfare. I mentioned Japan as well because I see they have some things in place that are more private market or at least they don't get in the way as much when the market tries to solve scarcity.
A US double-wide is classes above most houses in Japan. Your standard Japanese apartment would be illegal to build here for a hundred different reasons. A Japanese single-family home, I have never seen such construction anywhere in America to such low standards--no central HVAC even in the North where it's freezing. But if it's all that you can afford, you would probably rather have a house than no house.