Somehow, it is natural to not only accept a child as a possible hero of a story, but for me at least, to accept a child as the default hero of a story. All kinds of fairy tales and even ordinary fiction have child heroes, even those that might not necessarily be intended for children. Why this is is somewhat puzzling, but easily explainable. In my opinion, so much fiction is intended for children, in which the authors of the fiction or the progenitors of the fairy tales want the audience to sympathize with the protagonist. As a result of this, even tales intended for adults sometimes follow the trend of choosing a child hero, perhaps to invoke a sense of nostalgia, or perhaps just because that's the way fantastical stories have always been. A child protagonist can also be a blank slate: in many regards they can learn lessons and morals throughout the story that no adult could easily survive without already having a grasp on.
That being said, children have varied roles as protagonists in stories. Take "Hansel and Gretel", the most well known of the stories we discussed in class. The children in this story are clearly the heroes, but they fulfill the blank slate role. They make mistakes and allow themselves to be tricked, they are completely fallible and subject to the same desires that any other starving peasant children would be. Though they attempt to use their wits by leaving a trail to find their way home, they make it with breadcrumbs, a mistake that would cause their adventure with the witch. However, the children learn their lesson, and eventually trick the witch to defeat her, and then escape using their newfound cleverness, I suppose. Though exactly what character aspect improved through their experience at the witch's house is questionable, it is clear that they have more initiative than they did at the start of the tale, and the treasures they bring back allow them also to foil the poverty that launched the story. This would be an example of one kind of child protagonist.
Another would be that of "Molly Whuppie", which is a very different type of child protagonist. Molly Whuppie is a child in name only, executing theft and successful plans near infallibly. In fact, this is notable in that her age is hard to pinpoint. There are no clues based on her behavior, and she gets married at the end of the tale. In a lot of ways, Molly Whuppie seems to be a child simply for the purposes of allowing children to sympathize with the story. She executes a plot to force the ogre to kill his own children, to escape, and then returns to steal his belongings and force him to kill his own wife for no reason other than she was promised rewards if she did so. All the while, she shows a remarkable prescience about how many times she will be returning to the ogre's lair, seemingly not showing any emotion in response to the ogre's plight or the fact that she was just chased by an ogre. Molly Whuppie represents in many ways the other type of child protagonist: the one who exists specifically to spoon-feed the tale to children. Her being a child is not relevant to the tale, and at the end, considering she gets married, she must no longer be a child.
Freud, through Bettelheim, would explain Hansel and Gretel through the idea that the children at the beginning of the story are completely at the mercy of their id. They are walking, talking bundles of primal desires and oral fixations. The development that they eventually experience is a transition, that leads to them embracing the ego and thinking rationally, allowing them to escape the witch and the forest, with this common sense manifested symbolically by the treasures they bring back with them. Molly Whuppie is harder to place, since Bettelheim doesn't describe her directly. Further, it is hard to describe her with Freud's ideas about child psychology, because in so many ways, she is not a child.
Overall, children appear to be the heroes of stories for the purposes of making those stories palatable to children, whether the purpose of making it palatable is to deliver a moral or not. Children can be used to make fundamental character development more believable, or simply to make the hero seem more plucky and brave for the acts they commit, regardless if the acts are any different than those of an adult.