^^^ It would seem reasonable if those numbers are correct and that small it would not be a difficult problem to solve?
What is the actual problem?
I know a woman with 4 kids who has been living on welfare for a long time. She had a nice house she was renting but we had a forest fire a couple years ago and her place was destroyed. Since then she and the kids have been in several different places, and I think they would be classified as "sheltered homeless" since they are temporary. She is doing this in a town that has gotten expensive, and has never had enough long term rentals, but she doesn't want to move somewhere else... so they keep bouncing around until a better situation arises. How would you solve that problem?
I think when most people think of the "homeless problem" it's when the homeless squat in public (or private) spaces. It's worse when they leave trash, piss and **** there, harass people and beg, etc. But even a bunch of people living in vehicles and parking on a public street and otherwise not bothering anyone... are still a problem. I mean, if you bought a nice house in a nice neighborhood, you would not want random people parking on your street. Business owners don't want random freeloaders parking on their street either... or camped in the empty lot nearby.
The easy solution to that problem is to make it illegal and enforce the law.
People who have debilitating psych issues or drug and alcohol issues, should be cared for and sheltered until they can function in society (if ever). This care should be nationally funded rather than the responsibility of the place where they moved to. In other words you don't get sheltered and cared for on the southern CA beach just because that is where you were found.
In my opinion homelessness is mainly a symptom of allowing corporations to be greedy and voters failing to hold their government responsible.
The socio-economic changes that have taken place for the last ~45 years are a very serious issue IMO. But conflating that with homelessness is a huge error.
Homelessness actually declined through the 2000s until an uptick recently. At any rate the numbers are minuscule. It's a sideshow and circus to distract people, like so much of the news these days. Changing laws to keep towns from enforcing rules regarding public spaces is a big cause of the "visible homeless" uptick, along with the covid policies which "encouraged" functional addicts to become dysfunctional.
The slow squeezing of the lower-middle class over the last 45 years has simply resulted in lower living standards. People get by with less. On average the change is fairly small, and has happened so slowly that it isn't glaringly obvious... and the pundits for the oligarchy can successfully confuse the issue. In fact most of the people effected now support the policies that have been causing this!
The ability to manipulate people with propaganda is far greater now than in the past, and it is accelerating. I don't see how that will change. I don't suppose the truth ever had much influence in human society, but it's super obvious that it has very little now.