"As many have said, people are on the streets for a variety of reasons"
"Presenting homelessness as a psychiatric condition really is as low as it gets ? ?   ?    ?    ?   ?"

Jim why do you always pick up the wrong end of the stick. To all but a fool the most vulnerable are those with mental issues. It would seem sensible in a caring world to start with the most needy.
You quote government as the problem.which one Irish, Americam, UK, or the entire UN? It is a social problem and a question of what society is prepared to tolerate. We no longer hang starving people for stealing a loaf of bread- We kid ourselves we are too civilised for that but we quite happily live in a dog eat dog society and cross the road to avoid upsetting our sensibilities.
It requires people to get severely pissed off with the realities before any government will sully their hands with the problem.
Try reading the links!