"Universal housing won't work, because some homeless people want to be homeless! They don't want to be confined inside walls!"
Okay, suppose that's true. If every person were allocated their own house/apartment/unit, they wouldn't necessarily have to stay there. If they're more comfortable in the great outdoors, they could still sleep outside, hang out outside, spend their time outside. But they would still have a housing unit of their own, in case they wanted it. They could stay there occasionally, maybe when the weather was bad. They could take a shower there, receive mail there, have family and friends over there. Even if they chose not to use it as most housed people use our homes, they would still benefit from having it.
All of this, of course, is beside the point that the overwhelming majority of unhoused people do, in fact, want housing, and even the people who supposedly "turn down housing" or "don't want housing" are actually turning down the intense social control they're supposed to submit to in exchange for housing. There's a world of difference between "I'd rather sleep outside than live in a prison where I'm denied basic human rights and dignity" and "I actively like sleeping outside."
"But sometimes people in subsidized housing leave behind messes of blood and vomit and feces!"
Yes. Humans are animals, made of flesh and bone and gooey bits. Animals have gross bodily functions. We bleed and vomit and pee and poop. All of us do those things.
Sometimes, people -- especially poor people, who may have gone years without basic healthcare, or even decent food or hygiene -- have health issues or disabilities that prevent them from things like making it to the toilet in time, or cleaning up after themselves. Sometimes assigned housing for poor people is badly maintained, and may not even have things like a working flush toilet.
So yes, people have gross bodily functions, and some people -- especially if poor and/or sick and/or disabled -- may not have the ability or resources to deal with that issue in a hygienic way.
So what, exactly, is your solution?
Because my solution is to make sure that everyone has housing with adequate, working plumbing, and that everyone has access to voluntary healthcare to address chronic medical issues like vomiting or diarrhea, to provide needed adaptive equipment like a bedside commode, and, if needed, to hire personal care attendants to help people with things like cleaning, bathing, and toileting.
Your solution is what? That people with digestive issues should have to live outside? So they don't throw up on your nice floor? Do you have any idea how inhumane that sounds?
Or that they should be subjected to some type of coercive "behavior" program, because untreated Crohn's disease is a bad habit that they have to be tough-loved out of?
Because you think poor people are... just sitting there soiling themselves because they're too lazy to go to the toilet? That's actually what you think, isn't it? It follows logically from the assumption that poor people are poor in the first place because they're "lazy." But two seconds of thought would show that it couldn't possibly be true. You just think of poor people as less than human.
You are also gross and leaky and fleshy. You also poop and pee and barf and fart and sneeze. You are, through no virtue of your own, able to manage your bodily grossness. You are no better than someone who can't.