Joker has killed kids before, the most famous of these is Jason Todd Robin, but even Joker had trouble with the idea of killing babies. In the Sarah Essen arc, he looks like he doesn't want to hold the babies hostage; he's not even smiling. The only other example I can think of is in the Batman Who Laughs Elseworlds, where Joker's trying to push Bruce to finally kill him, and it works after he lines up dozens of parents and their children and shoots the parents and then poisons the children with Joker venom.
Harley has killed kids; she put bombs in video games and gave them to kids and then just detonated them for giggles.
I'm not sure about the others.
I agree that pushing the envelope like that is stupid. The super villains are supposed to be a threat, but they're also supposed to be people who can be rehabilitated. Writing stories where they look truly irredeemable messes that up. At this point, though, I've just accepted that it's bad writing. They can't think of any good things to do with the characters,so they make them do something unnecessarily depraved. The exception is Joker, for whom killing a kid, Robin, is a major part of the character's history with Batman. Even Joker doesn't make a habit of it, though, and he once rescued a child from a super villain who might have had nefarious plans for them. There was no reason for it, except to show up the super villain who was trying to act like a superhero; I guess it was Joker's way of saying "I'm more of a hero than you!" It was kind of like the "Joker hates Nazis" reveal in Batman vs. Captain America. Now, that's good writing! I wish they made more comics with fun twists like that, where I think I'm going to read something awful and depraved, but "surprise! everyone's okay!" Joker makes a fun wildcard. We get that he's a depraved super criminal; that's not why we like him.