Earlier quoted context omitted.
I've heard it called the homelessness industrial complex, that was from some City Journal article someone posted to HN some years back that introduced me to that publication. It was a shocking thing to contemplate but yah with that sum of money what exactly do we have to show for it?
If you're being paid by the government to manage homeless people, your incentive is to keep them homeless. Else your contact would end.
Even if we were looking at this from an utterly cynical, purely financial viewpoint, the people paid to help the homeless are effectively property managers and they benefit from housing the homeless, not letting them sleep on the street.