It won’t work. For starters no neighborhood wants any homeless housing units built in their areas. Second, the housing units cost a fortune, they couldn’t build enough of them. Third, even if they could figure out how and where to build enough units, they can’t force the homeless to move into them.
They have already tried much of this, and guess what - the problem got worse. So what do they do? Dump more money into it, of course.
Redistribution of income and wealth.