I think it works for Batman specifically because of his origins. However, while I think that Batman personally shouldn't kill, I don't like how writers sometimes have him force that onto others. For instance, he would actively PREVENT the Huntress from killing Joker. That's going too far. Actually, I liked DCAU Batman's views of this. He didn't kill, but he was ok with Superman killing President Luthor because he felt that "it had to be done." He suggested that Terry should kill Superman after he went rogue if he couldn't be stopped any other way. That's the right idea imo.
When it comes to matters like that, I would think that at the end of the day, the real people that should be blamed for all of this is the law system within the comic book worlds, both in books and in animation portrayals.
I mean, I can't see why any government would want to waste resources in keeping dangerous people like the Joker alive after he, along with several high profile criminals manage to escape their imprisonment and cause more chaos, leading to the deaths of countless more innocent lives.
I mean people have been executed for smaller reasons, and yet the Joker and Lex Luthor are kept alive? And I really wouldn't buy into the whole plead for insanity part either because that'd be just ignorance from the court system within the comic book world as well.
Honestly, if we had a figure like the Joker within the real world that constantly caused the level of trouble that he does within the comic books and is still only punished by just being placed within a prison cell for every time that he's caught, there would be a huge outcry from the public that would demand for his execution already.
Heck, even in the "Injustice Gods" story line, while Superman is also in the wrong zone as well, he did make a good point that Batman should have taken cared of the Joker a long time ago so that he wouldn't have been able to be a problem for them in the present.
If they don't have the balls to execute them, then just place them within the Phantom Zone.