>Quite a few cities have actually solved this problem. They provide housing and all of the additional services, like hygiene facilities, food, and security. Granted, they only solve it for certain cohorts, but it demonstrates that it is rather trivially solvable. That's going to lead to hot political quarreling, so it's a good place to stop.

Most of those services are available AFAIK, there's charities in most major Canadian cities that provide those basics. Without them the homeless population would probably be triple what you can see, and from what I've heard the majority just need it short term to get back on their feet.

But they can only offer those to people without substance abuse problems (drugs and alcohol are banned in those shelters), and those are the folks you'll mostly see out and about. You'd need some sort of institution with far greater resources to handle those, like an asylum. North America just seems to have a sordid history with the like.