You have to be careful, because what you said is also the standard argument against action. You get people implying that if you can't help everyone you shouldn't help anyone, that more study is needed before doing anything, et cetera. No solution is perfect, but they are all better than nothing.

And all homeless have something in common: they are homeless. Yes, most of them have other problems in addition, but once they have housing they have one less problem and the other problem is likely to be easier to treat or handle once they have their housing situation sorted out.