Well if we're talking about should Batman exist at all, no. Either as a ultra wealthy individual or freelance crime fighter. I'm just saying in the universe of Batman (setting aside DC overall which raises more issues) it doesn't make sense that Batman is like "I'm a vigilante, but I'll let these known repeat murderers off easy." He's already taken the judgement of good/bad on himself rather than let democratically appointed actors handle things. So if you've already taken that step what's the fetish for not using a gun?