Yeah, to eccho Marduk, the homeless are already extremely expensive, both in the direct spending already direct at them, and all the small bits of damage they do to general society and a well functioning urban area.
To take the LA homeless problem, there are apparently about
50,000 homeless in LA. Lets say you wanted to use the most brute force method and just steadily arrest all of them for various petty (and not so petty!) crimes: housing a criminal in prison costs about
15,000 to 70,000 dollars. Assuming the highest number of 70,000, imprisoning all 50,000 homeless in LA would cost about 3.5 billion per year. This is about 0.35% of LAs GDP to very decisively solve the homeless issue, and this is assuming some relatively high costs. Shipping them off to Alabama prison at 15,000 per inmate would be a less than a billion dollar fix. And this assumes you have to arrest all of them to fix the issues had with them! An only marginally more aggressive enforcement system would probably make LA much less desirable as a location to go, and force the Homeless who stick around to be better behaved.
Homeless is actually an easily solvable problem, which is why, even with how "progressive" many laws are now, most cities don't have a major homeless issue.