To be honest, I don't know much about homelessness in Japan besides what little I've read online, and what I actually see in public (and considering how much I walk around different places, I do see a lot of places). Anyway, I suspect this is probably another case where America spends a ton of money on stuff, but does so poorly and with bad effect. Just look at healthcare: the US spends far more per person than any other country, but outcomes are pretty lousy on average because it's so unequal and because treatment costs a fortune compared to anyplace else. I'm sure many other spending comparisons between the US and other nations are similar. How much money has the US spent on high-speed rail in California without getting much done?
I don't know what your point is, but the USA also spends tenfold on infrastructure per km with vastly worse results, and has the highest spend on healthcare per capita, with one of the worst outcomes in the developed world. So just spending more doesn't mean much.