Also, I would be REALLY pissed if I lived in a town where I had to struggle to make rent on a place I don't own every month, and the city is giving away free permanent houses to folks who don't have jobs or pay rent... I mean, I want homeless people to have homes, but if they're getting one for free and the economy continues to have housing prices way out of the reach of someone like me, I would be fucking pissed.
This viewpoint pretty well summarizes why homeless people aren't helped. Homeless people are viewed as "what happens when you don't have a job or stop paying your bills". Trust me, the fact that you work hard and pay your bills isn't what's keeping you off the street. It's your (relative) mental health and your network.
It already happens. My first apartment was a studio in a new downtown building that, with parking, I paid about 1/2 my monthly income for. Then I met my neighbor, who claimed to have been hurt by a city bus ("they closed the door on my arm"). She had a 2-br place with a terrace, and paid less than half of what I was paying.