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I headcanon that the reason Bruce never killed the Joker wasn’t strictly due to his moral "no-killing" rule, but because he physically couldn’t. It wasn’t a matter of choice—something, beyond anyone’s understanding, simply wouldn’t let it happen.
After Jason's death, Bruce was consumed with grief and rage, hunting the Joker with unrelenting determination. When he finally found him, he threw a batarang with his characteristic precision—only to watch it inexplicably graze the Joker’s throat. The cut was superficial, no worse than a shaving nick, leaving Bruce stunned and frustrated.
This wasn’t an isolated incident. Later, a vigilante fired two shots at the Joker. Both bullets should have been fatal; eyewitnesses swore one hit him square in the chest, directly in the heart. Yet somehow, one bullet missed entirely, and the other lodged harmlessly in non-vital tissue. The Joker walked away injured but very much alive.
On another occasion, the Joker plummeted from a skyscraper—a fall that should have shattered his body. When his enemies checked the impact site, there was no sign of him. Days later, there he was again, committing crimes as if nothing had happened.
It’s as though the Joker’s superpower is "plot armor," shielding him from death, but not from injury. No one in-universe consciously recognizes this; they attribute his survival to improbable luck, assuming that eventually, his luck will run out. It never does. Every attempt to kill him, whether by Batman, another vigilante, or sheer circumstance, fails in ways that defy logic.
The plot armor isn’t perfect. The Joker still suffers grotesque injuries—gunshot wounds, broken bones, disfigurements—but he always heals just enough to return. This strange phenomenon leaves Bruce trapped in a battle he can never definitively end. It’s a cruel irony: the Joker's survival is less about his cunning or tenacity and more about a mysterious, unbreakable force that keeps him alive, as if some cosmic law demands his presence in Gotham’s story.
TL;DR: Bruce doesn’t kill the Joker not just because of his moral code, but because he literally can’t. Every attempt to kill him fails due to the Joker’s "plot armor." He survives fatal injuries, improbable accidents, and direct attacks, leaving everyone to assume he’s just absurdly lucky. The truth? His "power" ensures he can never die, though it doesn’t save him from terrible injuries.