All the characters live in a world where the DO is bound to get loose and make everything horrible. And this will happen over and over again no matter what. The Shadow's stain on normal life even happens in turnings of the Wheel in which there isn't any channeling. So really, the Children should be blaming the Creator himself for the threat of the Shadow. That would make sense.

Blaming the channelers for unleashing the DO is like having a house built by lousy contractors, then blaming your slightly overweight friend for sitting on your kitchen counter and it breaking apart. Yes, the friend's weight and choice of seats caused the actual destruction to occur, but the contractors are the people who set the whole situation up with their incompetent behavior and choices. Most reasonable folks want to put the blame where it's due; unreasonable ones want it to go anywhere - especially anywhere that absolves their own errors and omissions.

If anything, blaming anyone - even the Creator - for the Shadow's appearance is a waste of time. Why? Because it misses the point that they still have to fight an incredible and difficult battle. Why waste time assigning blame when you have an immediate crisis to deal with? In the 80s, it was often said that American companies would waste time finding a scapegoat, whereas Japanese companies would focus on identifying and resolving the problem and its causes. That logic holds well here, too, as far as the Children and their distrust of the One Power.

The Children may have started out as a cool, philosophical, anti-Shadow society. They turned into a misogynist bunch of blood-thirsty asses who stuck their nose in everyone's business, by threat of torture and spite-inspired accusation. They don't even do as much good as the AS, who do things like Heal people that they don't "need" for anything.

All that said, yes they probably will duck their heads and charge at the Shadow without much complaint. Yes, the AS probably will take up the DR's precious time with beratings, accusations, and unnecessary formalities. This is because the AS have a great bargaining position (they WILL be needed at TG), whereas the Children have managed to make themselves more irrelevant and ignorable with every pious, pompous, self-serving accusation that they have instigated/inspired.