Yes, they should stop making storylines and character thought monologues and whatever about questioning their no kill policy, it only has ever served to highlight the absurdity of the concept and insult the intelligence of the viewers. When the superhero media ask the question "is it wrong of this superhero to throw this mass murdering lunatic in jail instead of killing them?" the answer that any remotely sane member of the audience thinks is "YES!!! KILL THEM ALREADY!!!". A person would have to literally be insane to think that any superhero would not be justified in serving as the judge, jury, and executioner of any member of the rogue's gallery of any superhero, especially after they break out of prison over and over again. The worst storylines are the ones that try to justify the no kill rule by having a superhero kill once and then rapidly devolve into totalitarian dictatorships and killing people for jaywalking and other extreme crap like that, it just shows that those super"heroes" were completely insane from the very beginning. A sane person (as in most people) would be able to kill someone like the Joker or Lex Luthor or any other of the rogues without even inching down the slippery slope not to mention jumping straight off it, it would take someone that was already a total nutjob to so adamantly refuse to kill those people in the first place and even more crazy to then turn around and start killing left and right. It's a nonargument to say superheroes shouldn't act as judge, jury, and executioner when dealing with villains that have killed as few as hundreds and as many as billions, there's killing a random mugger and then there's killing people like the Joker, a sane person wouldn't do the former and would do the latter without a second thought.
By it's very nature there is no sane reason for the no kill rule to exist in-universe, as mentioned by others the only reason for it to exist is to keep villains around so they don't have to keep making up more, and the rule as been around so long that writers are scared to truly deviate from it. It doesn't help either that the fandom is adamant that it stays in place no matter how little sense it makes for Superheroes not to kill, this is why we see people whining like crazy that Superman killed Zod in Man of Steel despite the fact that it couldn't possibly have been more justified nor unavoidable. However, even that isn't justifiable at this point. It's not as though superhero media can't have all superheroes at least try to kill their rogues all the time, it's just that that writers don't want to. Writers could do it, they'd just have to make use of legacy characters, near deaths, apparent deaths, the numerous examples of sci fi and fantasy resurrection and rebuilding technology in that universe, and simply have the heroes fail to capture or kill the villain sometimes. You know, actually have the hero LOSE sometimes as a good story would?