Batman does kill his enemies. Rash-al-gul for example. He killed him through inaction.
If batman believes the enemy can be saved, then he will try to save them.
Hence why his enemies go to the asylum, instead of a actual prison.
Because he hopes on day, they all can be redeemed.
For those, who are just pure evil, like rash-al-gul on the train to Wayne corp. Batman said these words. "I am no executioner, but that doesn't mean I HAVE to save you from yourself. "
