Bruce Wayne has Bezos level money. More, actually, IIRC. He literally could just end homelessness in Gotham. Permanently. And still be one of the wealthiest people in the world.
Crime, especially violent crime like muggings, is directly and inescapably related to poverty, marginalization, and lack of opportunities.
And again, it isn't about crime "going away", it's about reducing crime to the point where all that remains is extremely rare street crime, and white collar crime. I don't have the research in front of me, but IIRC basically 0% of muggings and similar crimes (armed robbery of a store, car jacking, etc) are committed to people who aren't living in poverty.
Batman isn't the punisher, even when he does kill people. His goal is to end the state of people not being safe in Gotham, to end violent street crime and other rampant forms of victimization. Targeted action against organized crime combined with economic justice action as Bruce, a guy who could purchase half of Gotham and still be a in the top 100 wealthiest individuals in the world, could accomplish that.
It would take years, perhaps even decades if enough powerful people are opposing him, but hey, that's good for a comic, right? Plenty of time for him to train up a whole Bat family, set them up to be independently wealthy so they can spread out eventually and do the same elsewhere while also using their wealth to gain political influence in the nation's greatest cities, and use that influence to make the change they are spearheading more sustainable with local, state, and eventually federal, changes.
Hell, fact is, at some point, Bruce has an obligation to get into politics, even if just indirectly. Social and economic action has limits (though far fewer for someone like him than for nearly anyone else), and are more effective when combined with political action.