Batman knows it, but I'm sure he's equally aware that he cannot possibly continue his career if he makes a habit of murder. Bear in mind that unlike the police, Batman isn't a duly appointed representative of the State. He's already gone above and beyond his duty to his fellow man and to ask more of him is pretty pretty selfish.
If anyone should kill Joker, it ought to be the people who know he won't stay locked in their cells, that their treatment is useless and know that eventually, he will slip away again. They're in a better position to do so and it would have far less impact on them emotionally than it would on Batman.