Honestly this isn't the right conversation to be having at all.
In the United States, ~40% of the homeless are employed. A deeply non-trivial percent either are kids or have kids. Everyone should volunteer at a support center for homeless youth some time.
Sure, there may be some kind of Pareto principal in play for the hardest 20% of cases to crack. Who cares? Let's eliminate 80% of the existing problem and worry about the rest when we get there.
I'm going to go out on a limb and suggest that the median HN reader has very little appreciation of the human reality of homelessness in the United States, and primarily see it through the lens of people at the extreme, visible margins. I know I used to until I got involved.
edit: I mean all of this in a very boring, matter of fact way, not some kind of holier-than-thou virtue signaling way. The 80% problem of homelessness is a tractable economic problem. While it's true that the United States has an almost dizzying level of propaganda demonizing poor people, it's also true that real homelessness is hard to spot because people have a natural instinct to preserve their and their family's dignity. The first time I came to terms with this was coaching debate in highschool. I had a varsity debater who couldn't afford pants to meet the dress code. Incredibly bright, academically successful kid. His father was an unemployed teacher working menial jobs, his mother was taking care of three kids. They lived in a tent at campsites. I had absolutely no idea. We obviously bought him pants and paid all his travel/etc. fees (he'd been making excuses to not go to events requiring travel). That's a very boring, normal case.
That family should have had a free or nearly free housing option. They did not. They still wouldn't.
And then there are people who aren't families, without the knack for conveying a moving story, or exceptionally good in every way but unfair circumstances.
Many of these people, and not just the really, really bad nuisance ones people use as excuses to superiority, are literally slaves, performing the scarecrow work of deterrence as living examples, for "society", for no pay.
I think this is an injustice, subverted by its own cruelty, and one of the more compelling arguments for UBI.