I have no issues with this at all on the municipal level. It's worthwhile as an experiment, and if it works as a part of a solution, perhaps other cities will follow suit.
Homelessness is a major problem. First of all, as Jim mentioned, a huge percentage of these people suffer from severe mental disorders, and another large chunk are veterans who were never able to reassimilate after returning from active duty. These are people we don't want slipping through the cracks. These are the people who we should be helping.
To address some of Chef Jim's concerns, I don't think it's a one size fits all solution; but I certainly believe it could help in many cases.
Many people who have disabilities and become homeless, are to some degree or another missing persons. They have available support networks from people who genuinely want to help them, but have no idea where they are.
I think that this, combined with some of the other things Jim suggests could be effective, implemented at the municipal level.