"In most of those situations, the lack of shelter is a symptom of a much more profound problem."

I disagree. The lack of shelter is the problem. Experience in various cities and a number of studies have shown that a "housing first" policy works, and it saves money. Do an Internet search on "housing first" and you will find a lot of material on this. Here is a link to one article:

https://www.washingtonpost.com/news/inspired-life/wp/2015/05/06/meet-the-outsider-who-accidentally-solved-chronic-homelessness/?tid=sm_fb&utm_campaign=buffer&utm_content=buffer4fc83&utm_medium=social&utm_source=facebook.com