Personally, if a guy looks like he's in rough shape and asks me for a drink, I might oblige him. Not because I think it's helping him in the long run, but because it could help him feel better now.
(And I don't mean to be critical of your position, just pointing out that it might not be neutral in the long term.)
When people aren't using the services there's always a reason. You might not find that reason valid ("well then they should just quit" etc) but it's there. An addict on the street isn't having a better time than you would be doing the same thing. You have to consider why they experience that as a better option for themselves than the one you're presenting.
That is what I was saying. There is the perceived return on investment of using the services designed to help get one out of homelessness, and it is being weighed against the perceived return of going back to the street. If you can bring in several hundred dollars a day on the streets that you can spend on alcohol, the effort of being in a place that is trying to help you change your situation might be hard to justify.
But a big piece of the equation is how easy it is to just get cash from well-meaning people on the street.
I'm not disagreeing with you about needing help with addictions, but there are two sides to the equation.
Very much this: The long run is vague, and the only sure thing is that we will be dead. But this is a small thing one can do now.