Vagrancy laws in the United States were dramatically expanded after the Civil War, to restrict and control the recently freed slaves. In some cases, the penalty for vagrancy was to be forced to work for someone for free.
(Imagine if you were a recently freed slave, trying to escape the place where you were enslaved, traveling around looking for separated family members, and then that happened to you.)
The unique appeal of a vagrancy law is that it doesn't require a crime to be committed, so it becomes possible to outlaw certain kinds of persons.
Now in the 21st century there's a whole new set of reasons why people become homeless. And I'm not saying that it's easy to deal with encampments in public.
But many of the solutions to these problems are already ruled out in the USA. And that's precisely because the US has attempted to carry on slavery by other means. If you look carefully, you can see that the American obsession with punishing the poor or the sick almost always derives from fear of a racialized underclass. Thus it's impossible to make a public space welcoming, because you-know-who will benefit. It's impossible to make public health good, because you-know-who will benefit.
Not everyone who believes in these ideas today consciously knows that these ideas are racist in origin, but that's definitely how they started.
P.S. of course now the US is such a dysfunctional kleptobureaucracy they can't even deliver bus shelters, literally the simplest possible permanent structure, even when they say they're trying to undo racism