The data are pretty clear that those who are not drug addicts end up coming out of homelessness fairly fast by making use of America's numerous social programs. The story of American poverty alleviation is a resounding success.
Drug addiction and mental illness is another story.
No, that is not what I'm saying. Notice, I never said we shouldn't do anything.
I'm saying reaching the state of "no homelessness" is dependent upon finding something to do with the worst of the homeless.
For a tech analogy, imagine you've architected a system that has 99.5% uptime. You might be able to imagine a way to get to 99.9% up time.
With enough resources, you might even be able to get to 99.99% uptime. With laser focus and a giant dedicated team and an immense budget, maybe you can get it to 99.995%.
But what would you do if some exec came in and said we need 100% uptime, and we are a failure as a company unless we reach that?
Drug addiction and mental illness is another story.