Ok putting all this aside for a moment. If you just give someone a place to live you solve many immediate problems. The social worker knows where they are, the food stamps can be delivered right there, you get them out of the elements, any type of medication and you know where it is supposed to go, sanitation is also taken care of if nothing else they can shower.
So right it isn’t an end all be all solution. You can easily have a whole bunch of underlying issues my point is you already got them housed you rid them of a whole mess of problems at once.
Just a fyi. I had a month from hell once and ended up homeless. It was amazing how fast I lost everything. Ended up living in my car until I could I could rebuild. The thing I wanted the most was a clean shower and a change of clothing.