There's a difference between children dying as part of the narrative of a game, film or book, and the game allowing people to hunt them down in whatever creative manner they see fit with no consequences.
The OP question is 'should children be allowed to die in games?'
I say yes- if caught in dragonfire, or attacked by NPCs etc- it allows heroic players to try to protect them, and fail. Also there should be a game world reaction to all npc death, rather than people just stepping over the corpses as if they aren't there. The only dead things the population of Skyrim discuss is dragons, not bob the baker, local well-liked everyman, when he is left naked in the fountain. The thing is players are inherently brilliantly creative and would end up luring monsters in to kill children in that situation anyway- it would be cool if, in that case, you were blamed for bringing death upon the town.
If the question is 'should players be allowed to murder children just because they find them annoying?' Then I say only if the game world has a penalty other than 'pay a thousand gold to get away with it', and even then I wouldn't want to be on the dev team, having it brought up in every interview I went for, being asked 'why did you let players do that?'.
I wonder if the problem is that the in-game penalties for all capital crimes are practically worthless, they just cost you money or two minutes of time with no long term social penalties, as its far more important that they don't want to slow down players too much who make a mistake or are just experimenting. Would players still want to kill kids (or anyone for that matter) in Skyrim if, the first time you were caught, a message was sent to all holds saying you were a child-killer and a deviant? No shop keeper would serve you, no inn would let you stay, your old companions would treat you with revulsion and disgust, and the Jarls immediately seized your property and threw you out. Your defence of 'the Jarl's daughter didn't trust me so I killed her' mysteriously carries little weight, and both he and his men attack you on sight for the rest of the campaign. You'd be a hated outcast, living in the wild, with contacts and 50% of the quests lost forever, as no one trusts you. How about that? Same goes for murder- if you had a long-term reputation that had negative effects rather than positive ones of owning the loot of the dead, maybe it wouldn't be as appealing if the social consequences were more realistic, and maybe not as much fun.
People want to be able to do what they like with few consequences, thats cool, its a game, but if we argue for realism, I'm also ok with game worlds having realistic approaches to crossing moral boundaries, even if it costs the player access to content. I have no problem with NPCs not trusting a serial killer with their holy magic sword to save the world, and that's something I hope next gen systems get even better at in terms of role-playing games- I'll take a game world like that where the player isn't an all-powerful creature that can treat everyone as their plaything over even-better graphics any day.
However, I take people's point that some of the kids are very annoying and repetitive in thier dialogue. If anything that's the most realistic thing about them. Maybe big bad dragon hunters can shrug it off.