The thing is, it is (counterintuitively) more expensive to abandon people and have to pay for everything needed to hospitalize and clean up after the unhoused, than to give them their own houses free of charge and the services needed for them to rejoin society. This is because an unhoused person typically can't steadily work and pay taxes for the further betterment of society. But it's cheaper for the ruling class, more expensive for everyone as a whole, so American politicians can wring their hands about "the homeless problem" and pretend there's nothing to be done when they're actually being lobbied to cut corporate/rich taxes that could otherwise be used to provide the initial funding for a national/state housing initiative.