I remember seeing favelas in Brazil next door to ultraluxury apartments 10 years ago thinking that this is probably what the future of the US was going to be like if wealth inequality steadily kept climbing. And here it is. r > g in the flesh - the other side of "the magic of compounding".
I'd say that many of the homeless are homeless because they could not live in the society. This is why they ran out of money and housing, not the other way around. What could help them is psychological / psychiatric treatment, rehabilitation from addictions, and offering some better prospects in life than to get wasted every day. This is not a (purely) money distribution problem.
Agreed, it's a much deeper issue in modern society.
But treatments like those you mention are not a complete solution. They're a sticking plaster on a wet wound.
Society will need to change at it's core and the issues show worse in places where the biggest changes are needed.