Like why exactly is it Batman's responsibility to kill Joker? Joker isn't some sort of supernatural being that can be only killed by Batman.
Rule .303. Batman has the capacity to find, thwart, and apprehend Joker on multiple occasions and he knows,
canonically, what is going to happen each and every single time he apprehends the Joker. That means that he bears some degree of the moral responsibility for the inevitable consequences of taking Joker in, alive, and allowing Gotham's "justice" system to fail at its job.
Batman's also a good example, though, because
canonically he also knows-- to some fair degree of certainty-- that the long-term consequences of him, personally, killing the Joker would be worse than the Joker's cumulative lifetime of rampages. He knows that an obsessive billionaire who dresses up as a rodent to beat up the mentally ill is only a
thin red line from belonging in Arkham himself, and that his powers and training would make him more dangerous than any of his terrestrial enemies if he crossed it.
He's not wrong. He also knows the kind of heat that would bring down on his "batfamily", who are mostly normal human beings operating by the grace of the same corruption that makes them necessary.
It's an interesting moral argument, born out of a Doylist need to justify a faintly ridiculous Watsonian character trait that was imposed upon the entire genre of superhero storytelling by external moral hypocrisy. (And, you know,
marketing.)
On the other hand, when he threatens to suicide-bomb an entire planet full of sentient non-combatant aliens to stop Darkseid, neither his allies nor Darkseid himself is willing to
call his bluff-- because they all know, to the last person, that Batman is not bluffing. This is also the right call; Earth is not the only planet full of sentient non-combatant beings that Apokolips is currently/always a clear and present danger to.
Doesn't really apply to Spider-Man, whose
technical pacifism is frequently expressed in a way that makes it look like narcissistic martyrdom. Marvel's bent over backwards to give it the Thermian explanation that Spider-Man is attuned to the Web of Life, and that failing to uphold his commitment to always saving everyone possible would mean spiritually losing his capacity to save lives. It's kinda hokey, but I use it myself in some of my own Marvel storytelling. However, that's a
relatively recent development that is largely not held in high regard by other hardcore Spider-Man fans.
And in a fictional universe where Spider-Man's magic powers weren't attached to a load-bearing pillar of morality...
In modern society vigilantes shouldn't execute people(that just opens massive Punisher shaped can of worms), if Gotham really wanted to get rid of Joker well they live in part of america were execution(as distasteful as it is) seems to be legal.
I'm not talking about execution here; conversation started with refusing to accept the surrender of a goblin combatant. Most of what comicbook vigilantes do is highly illegal-- looking for and beating up people
planning to engage in crimes breaks all sorts of laws, and even by the laxest legal standards of self-defense, no individual has the
right to kill another individual.
It's funny how comicbook fans can watch their heroes commit violent crime after violent crime, maiming other (only sometimes) violent criminals who have a right to a judge and a jury, and it's only when they do what is perfectly legal and moral-- using lethal force in direct defense of their own, or another's, life from clear and present danger-- that we, as comic book moral philosophers, kick up a fuss.
Second thing is that in real life, prison escape isn't as common as in comic books
Like is it really superhero's fault that superhero comics run on "Okay, this villain is popular so bring them back for another issue! Yeah yeah just say they escaped or something" logic? Like from in universe perspective, if people keep escaping from prison then there is something severely wrong with prison itself. Like why DO they don't just destroy Rhino's suit or keep it located in another facility?
Well, point blank, Batman doesn't have the means to fix Arkham Asylum or Gotham City's notoriously corrupt police department. He's not
capable of making everyone else involved
do the right thing. He does not bear
more responsibility for the Joker's third-and-subsequent crime sprees than the Joker himself does, or Gotham PD, or the faculty and staff at Arkham Asylum. He's just the only person who ever has the
capacity and the
authority to do so at the same time.
He chooses to take the Joker down non-lethally, when this presents more of a risk to the Joker's victims, and it's only because the writers bend over backwards-- for good reasons!-- to avoid calling attention to this that... well, we aren't constantly having our attention called to it. In a "more realistic" adolescent power fantasy, Barman and Spider-Man would have watched countless innocent people die while they were walking on eggshells to protect people
literally in the act of committing murder.
I'm not suggesting that we change the conventions of the superhero genre, though that's already happening on its own. I'm just saying that we shouldn't mistake them for real-life moral principles or worse, apply them to genres or heroic storytelling that lack all of the modern and/or historical context that made those convenitions apply to superhero stories in the first place.