Chess + Wu Tang Clan = WuChess

There is a much more basic probem if Batman starts killing all the evil opponents in self-defense.
After terminating the first 25, Bruce Wayne can only return home to wayne manor with Batman retiring.
DC would never allow Batman to retire, or even Joker to die, as long as there is a spark of "-quel" in it.
Under this assumptions Batman is more instinct-controlled and more predictable than Paramecium.
Similarly non of the evil Creatures will ever be able to completely win over batman or to get destroyed... cause maybe they need to return in one of the "-quels"...
Similar Batman and all the villains never age...

There is also a common theme in Batman that being a criminal is an illness and is curable. Batman truly believes this. This was even explored in The Dark Knight Returns where the Joker feigns sanity. Contrast this to Superman who believes that being a criminal is innate and that the only means of stopping a criminal is permanent incarceration. And when criminals have been "redeemed," Supes is hesitant to accept it.

he killed him at the end of the Killing Joke...

It's implied in Richards' paragraph, but their repeating cycle also helps underscore that the struggle between Good and Evil is Eternal.

I think the petty thugs fear Batman because he threatens them with pain, not death also Batman is supposed to be the embodiment of fear.

I don't think Batman should kill the Joker but I think the Joker should be tried in a court of law and sentenced to death even if he is insane.

Batman doesn't kill beccause killing is easy. Plus, if Batman were to kill, where would it stop? In a court of law, when a prisoner is put to death, it is done through the justice system. If Batman were to kill, he would truly be a vigilante, someone who works outside the law and becomes judge, jury, and executioner. In addition, it would be out of revenge not justice. Batman at one time was a duly deputized agent of the law. Though his methods were questioned at times, he worked within the law to bring in those criminals that the police could NOT handle. The police sometimes hunted Batman because of a misunderstanding or because someone tried to frame him, or because Batman wanted to appear to be the murderer for his own reasons, but Batman always followed the law and brought the criminals in for trial. And it wasn't Batman who would send the Joker to Arkam. It was the police and the justice system who decided that. Batman wants the Joker sent to JAIL to pay for his crimes, but because the Joker is declared unstable, he is sent to the Asylum instead, but that only gives him time to plan his next move. If he were jailed for his crimes, he would be placed on death row. But the Joker is the perfect foil for Batman. He challenges the Dark Knight to do his worst and his best at the same time. He doesn't care who Batman is, only that he can do what he feels that will cause Batman pain, pain such as killing Jason. The Joker sees all of Batman's associates as a threat and an obstacle. That is why he tries to get rid of them. He wants to deal with Batman on a one-on-one level. And at the same time, he wants to see Batman in action. He has respect for Batman that no other criminal besides Ra's al Ghul has.

These are all weak reasons for Batman not to kill. "Because if he kills the Joker, the Joker wins"? is his ego worth the body count the Joker racks up each time he gets free (and he always gets free)? "Because after 25 (I am guessing his rogues gallery and a few others) he would just go home and retire"? Yeah, because it's not like the heroes that do kill are still putting out stories on a regular basis. What ,The Punisher, Wolverine, Wonder Woman, Aquaman, and others who do take lives are out of stories now too? "Killing is too easy" What this says to me is that Batman would rather challenge himself than keep the people of Gotham safe from the regular murder sprees commited by the likes of Joker, Croc, and the myriad gang members he faces on a regular basis. "He works within the law"? Are you kidding me? Dressing up as an animal, beating citizens brutally to the point of needing lengthy hospital stays, use of non regulated and unsanctioned wiretaps, computer hacking, use of military grade weapons and explosives (I don't use a gun, but I've got missiles on my car, plane, boat, and motorcycle), extracting confessions under duress of immanent violence (rendering them inadmissible in a court of law), and even driving the Batmobile on public roads without plates, registration, and insurance. Tell me again where this guy acts within the law? Read the character, watch his movies, love the hell out of the iconography and stay loyal to your interest, but don't kid yourself. Batman is a vigilante, despite his holier-than-thou attitude and good relations with Commissioner Gordon, he is no different from any other vigilante. Is it really better that he cripples people rather than kill them? Now you end up with former criminals with medical disabilities needing social support because some nutcase in a fright suite fractured his spine by swinging into it from the top of the fifth floor roof on his Bat-line. Do you think Gotham citizens like that their tax dollars are subsidizing palliative care for rapists and muggers. Face it, the only reason Batman doesn't kill is because DC likes to make money off reusing the rogues gallery. Morality through finance. Comics, people. :)