Tauriq Moosa at Big Think argues the case:

I think yes. Firstly, merely, say, debilitating him in some way is not helpful. What’s powerful is not The Joker’s physical presence but what he can create and conjure. For example, in The Killing Joke by Alan Moore and Brian Bolland, The Joker attempts to drive Commissioner Gordon insane – The Joker wants to show that anyone, given the right circumstances, could end up as he did. The Joker himself does not need to be there for this to occur. Gordon for most of the story is simply strapped to a ride, in an abandoned amusement park. Even if he was locked up or crippled, there is little doubt The Joker’s powerful mind could still pull on threads that run like veins throughout Gotham’s criminal underworld. The Joker after all is the decayed beating heart of crime.

Or in A Death in the Family, The Joker blackmails the biological mother of Jason Todd (the second Robin) to hand the boy over to him. The Joker proceeds to kill him. However, the blackmail and death need not have been performed by The Joker himself. The Joker’s access to and acquisition of information is what made him successful.

Secondly, Batman could make it such that The Joker’s death appears to be an accident. This means The Dark Knight can retain his image as a nonlethal superhero, but still have the chaotic force of The Joker forever gone.

It appears that Batman’s nonlethal attitude to The Joker is partially responsible for the continual death and suffering of many innocenets. This is so because we all know that Arkham Asylum – the revolving door of Gotham’s criminals – can’t hold The Joker. And, as I said, debilitating him doesn’t work and there is no cure for his chaos and insanity.

The question left unaddressed by Moosa that is essential to this discussion is: Why doesn’t Batman kill?

I’ve often wondered if it’s because he’s terrified he’ll enjoy it and not be able to draw the line after that. Batman is a psychopath. And we’ve already been shown what Batman is like when he kills – Rorschach. Now the question is not the Joker continuing to kill vs not killing, but the horrors of Joker killing on balance against Batman killing.