> What's to say someone else can't be eliminating the other classes of homelessness in parallel

You both can and must address everything in parallel to actually dent the "homeless problem".

That's the point.

Let's say there are 5 primary classes of homeless. Even if you take one of them and reduce it to zero (and you will never accomplish this)--you're still left with 80% of the problem.

Only now the people approving the checks are angry because the "homeless problem" doesn't really look any better.