$12,000 / year * 600,000 homeless people in the USA =
$7,200,000,000 / year

Maybe let's start small and help some homeless people get off the streets for the low low price of ~0.1% of the country's annual spending.

I assume that once you have a stable situation, the supreme gets cut off. As more homeless get off the streets, this number should decrease (but probably not disappear [my cynicism says that we'll probably never completely solve homelessness]). As more homeless become taxably employed, federal government revenue will increase; spending should decrease as various programs can be throttled back. I'm sure some sociologist-economist can give you a calculated estimated ROI figure on this investment, but I feel that the numbers would probably balance pretty evenly with the added benefit of helping a bunch of people and communities.

UBI would be great but I don't expect that to occur without a tonne of baby steps