I'm not suggesting that Batman would be a better hero if he started shooting people, but I do have to wonder how the people around him feel about his idealism.
Hey Batman. You know how you spared Joker's life a couple of weeks ago and then he escaped from prison again? While he was out, he burned down my neighborhood and killed everyone I work with. So... thanks for that. Dick.
The game opens with Joker in your custody. Not to spoil the plot or anything, but you don't just put him in jail and go home to enjoy a nice quiet evening of surfing the net on the Bat-computer and brooding. Between that point and the end of the game, about a hundred orderlies and prison guards end up dead. Nice one, Batman.