Everything would be all good if Batman killed the Joker, right? I mean, the Joker is the ultimate incarnation of evil in comic books, almost the spot on definition of Supervillain. Killing him would save a lot of lives. Right? Wrong. Here is why:
We know Batman is crazy, right? Yup. This all stems back from his parents death right in front of his eyes. The villains he fights he fights because of that one incident. In someways, the villains he fights represent the mugger that murdered his parents. Imagine this going into overdrive. He fights the Joker, sees and believes that HE is in fact the one that killed his parents. Fights him. And then throws him off a building. Happy ending?
Then, the preexisting order would fall apart. Once he kills him, other villains in Gotham would go insane (even more so), try and become the new big man on the street. Once gentlemanly villains like The Peinquin would go mad. Turn into a psycotic, baby killing murderer. And Batman would have almost no limits. Killing any criminal he see's intentionally. Even going as far as blowing up henchmen. This would go on and on until Batman kills Peinguin. Then it gets worse.
The public would of course disapprove of Batman's actions. So he would soon get plastic surgery and a new suit, thus a new start. But the Joker is still haunting him. He now sees every villain as The Joker. Two Face and Riddler would now be complete replicas of his greatest enemy. And he would stop at nothing to stop who he see's as the Joker, aka the one who killed his parents. And like that, the pain is gone. But it is replaced with something new: pure insanity. Batman will become the Joker.
He would again undergo plastic surgery. Get a newer, more colorful suit. Start making public appearances, and give off the illusion that he is a superhero. But everything in this new "Joker Vision" is worse. He now sees enemies as funny. He now sees the funny side. Everything, his suit, his partner, and his villains, is a joke. And to make it worse, he is so afraid of killing again he barely hurts criminals anymore. People like Mr. Freeze, who was once tragic, is now a one-line spewing muscleman.
So, in conclusion, if Batman killed the Joker, we would get Batman and Robin. And no one wants that. Thank you all for reading, peace out!