I...don't think Bruce just picks up random addicts on the streets and beats the shit out of them. I don't think that's what he does at all.
I think the issue here is patrols, where he stops things like muggings? GEE I CAN'T IMAGINE WHY BATMAN WOULD WANT TO STOP THINGS LIKE MUGGINGS.
Really though, his thing isn't a "war on drugs" or a "war on crime" or anything like that. He's all about defending people, especially people who can't defend themselves. While there may be Unfortunate Implications in what he does, those same implications would be there regardless of how much money he had, so long as he had more than they did.
Besides, he's a smart guy, and he recognizes the root of those problems is poverty. He also recognizes that the best way to address social issues is through his philanthropic work, as Bruce Wayne, rather than Batman. Thus, the Wayne Foundation, which seems to be there to address just these kinds of problems--problems Batman can't fix.