If you want to call it cowardice, sure, but he's absolutely right about this creating a moral slippery slope. It really needs to be understood that the instant he kills the Joker, his rule goes from "never killing anyone" to "never killing anyone, unless they're as bad as the Joker." But how do you define how "bad" someone is to cross that threshold? When they've committed as many crimes as the Joker? When they have the same neuroses as the Joker? How about when an entire group of people are working together to create as Joker-level problems, or if a person seems to be set on a path of crime that will lead them to Joker-level criminal enterprises?
The only thing keeping him from going full Punisher or Judge Dredd is his rule, which wildly impractical and fallacious as it may seem, keeps him grounded. He kills the Joker, and he knows he'd just become the inverse problem of him- a psychopathic billionaire with a god-of-justice complex.