Thought this was an interesting idea. Utah has done the math that the cost of jail and ER exceeds the cost of providing a home and a social worker.
This is their solution to the problem of homelessness.

Housing Works

Does this lead to an increased likelyhood of people abusing the system?
Is this a path to ending homelessness in a definitive way?
Is it sustainable?
Does it actually save the state money?

Personally, I am interested to see how this experiment plays out.