Batman's already the biggest anti-gun hero around, and he's DC's biggest hero by far. His trauma is a constant reminder to us all without having to get preachy about it. Having DC heroes try to affect legislation is a bad idea in-universe and out, unless it were just one storyline with an endpoint in mind. Actually changing DC earth (or America) would do that thing the main Marvel or DC universes avoid, which is making the world too different than our own. If they got rid of guns, then how would the comics address real world gun violence after that? Having Batman constantly reinforce his anti-gun stance in a world filled with guns makes more sense.