Consider the end of the Killing Joke. Joker's punchline is that neither men realize how crazy they actually are, and the obvious metaphor is that they're an allegorical Batman and Joker, with Joker claiming that Batman is just as crazy as he is, but I never understood the rationality for the claim before. It just seemed like unsubstantiated tripe.
Something I eventually realized, only a few weeks ago: the basis for Joker's claim is that Batman really, objectively has lost all sense of self-perspective by that point. For all his talent, Bruce Wayne is still nothing more than a vigilante. Remember, earlier in the book, when Commissioner Gordon told Batman that he had to bring in Joker "by the book"? That he had to show him "their way worked"? Seeds on stone. The threat of Joker has gotten so imprinted in Batman's mind that it's overwhelmed any respect or duty he felt he had to the criminal justice system. At this point, for Bruce, it's all about trying to stay a man with moral or just descends into murderous violence. But either choice he makes, whether to cross the beam or not cross it, the asylum is long gone. It never crosses Bruce's mind as he gives Joker his final chance that he doesn't have the authority to be Joker's arbiter of Fate as a man in a bat-suit outside of the law, and in that, he's just as mad as Mr. J is, which is exactly what Joker was going for all along. (To be fair, it's possible that Bruce Wayne never had a say in the matter to begin with. Constantly capturing criminals that constantly escape, only to re-capture them and get continuously put in prisons that never hold them? Honoring a system indefinitely that doesn't work? That, in and of itself, is madness, which means the only solution left against that "ordered" system would be to do something... insane. All Joker had to do was point it out.)
And at the end, I think maybe Bruce realizes all of this, which is why he laughs before killing him. Joker wins- fatality.