Joker’s Murders Actually Make Him DC's Most Effective Crime-Fighter
Despite his own terrible deeds, it's possible that Joker is also the most effective crime-fighter in the DC Universe, albeit with extremely dark methods. This is because the Clown Prince of Crime's extremely high body count is not limited to just the innocents of Gotham, as Joker has killed his fair share of criminals as well, eliminating rivals, enemies, and even his own underlings just for "fun." While the villains handled by Batman often break out of Arkham Asylum to inevitably cause more chaos (including the Joker himself), those villains who cross Joker usually don't get back up after he deals with them, and over his decades in the comics, that body count has added up.
Whether or not Joker can be seen as a "crime-fighter," it's hard to argue the fact that Joker is one of DC Comics' biggest killers, with one of the largest body counts of any other villain in the DC Universe, especially excluding cosmic acts of genocide where whole planets are taken out of play at once. In fact, Joker vastly prefers to get up close and personal, having achieved a horrifyingly high number of kills with bombs, guns, Joker Gas, lethal gadgets, and many other types of weapon.
However, given the circles he moves in, a huge proportion of Joker's victims are themselves criminals. In James Tynion IV and Jorge Jimenez's ongoing Batman run, it was revealed Joker murdered the Designer, putting a stop to the mastermind's plan to elevate Gotham's major super-villains to new heights. Not only that, but Joker has personally killed countless of his own thugs and henchman, as well as those of his fellow villains and rivals such as Penguin, Talia al Ghul, Riddler, Professor Pyg, and many more, often killing out of boredom. Joker is as happy to take out major villains as minor, consuming the demon Beelzebub, brutally murdering Alexander Luthor of Earth-3 at the end of DC's Infinite Crisis, and burying Doctor Hurt of the Black Glove alive after judging him an unworthy adversary.
Joker has also killed plenty of super-villains, including Shrike, Psimon, Iron Cross, fallen hero Oberon Sexton, and members of the Royal Flush gang, and even took a chunk out of the powerful Falcone crime family. Though it ended in a stalemate, the War of Jokes and Riddles from Tom King's Batman run made it clear that Joker is even prepared to kill Gotham's other villains if challenged. Of course, Joker is no hero - his actions and methods would be seen as terrible, immoral, and downright deplorable even by the most brutal vigilantes like Marvel's Punisher, and rightly so - but the fact remains that Joker has taken countless criminals and super-villains off the board, and with a permanency that someone like Batman can never achieve due to his no killing rule.
In a very dark way, the sheer number of named and unnamed criminals who have met their end at Joker's hands in the DC Universe suggests his strong efficacy as a crime-fighter. Of course, this is really only a side effect of the sheer levels of chaos, destruction, and death Joker brings, rather than coming from any sense of justice. Joker has taken countless criminals off the board, from his own henchmen to interdimensional threats, but he does so purely due to the whims of what he thinks is funny at the time. Joker is no hero, and he's undoubtedly brought more harm to the world than he's prevented, but taking his own misdeeds out of the equation, he's done a disturbingly effective job at permanently ending the threat of countless of DC's criminal figures.