Why in so many popular fairy tales and cartoons are the mothers always dead?

In The Uses of Enchantment (1976), Bruno Bettelheim, the child psychologist, saw the dead mother as a psychological boon for kids:
The typical fairy-tale splitting of the mother into a good (usually dead) mother and an evil stepmother … is not only a means of preserving an internal all-good mother when the real mother is not all-good, but it also permits anger at this bad “stepmother” without endangering the goodwill of the true mother.
You may notice that these thoughts about dead mothers share a notable feature: they don’t bother at all with the dead mother herself, only with the person, force, or thing that sweeps in and benefits from her death. Bettelheim focuses on the child’s internal sense of himself, Dever on subjectivity itself. Have we missed something here? Indeed. I present door No. 3, the newest beneficiary of the dead mother: the good father.

The author goes on to argue that the “dead mother making way for the caring single father” trope in cartoons is “misogyny made cute.”

I have not seen many of the animated movies cited in the piece, so I can't speak to whether the caring single father is really a culprit behind the ubiquitous dead mothers, but I can think of some other explanations that are credible as well:

Many fairy tales were written in an age when many more mothers died giving birth and so it was not so uncommon a scenario. Since many Disney movies are adaptations of those fairy tales, such as those of the Brothers Grimm and Hans Christian Andersen, they retain the basic structure of those stories, even as advances in medicine have reduced the risk of childbirth by an order of magnitude.
Mothers have traditionally been such dominant forces in running the household that they can actually shield a child from any extreme turmoil. That's good for the child but not great for the drama. An absent mother in a fictional drama lengthens the menu of credible external stresses on a child. You can have a mother present and still put the child into dicey situations, but then the mother just seems negligent, and that's often not the story the writer wants to tell.
In contrast, many single fathers are seen as not really understanding what is going on in their children's lives, often because the father is always off at work. Many fictional fathers are also seen as somewhat incompetent around the house. This, too, may become a more outdated stereotype as more and more women choose to pursue full-time careers while their husbands handle a greater share of child care duty.

If we want movies that really reflect this age, we should be seeing more movies that show kids having to move back in with their parents after graduating because the unemployment rate is so high. This sounds like fertile ground for an Apatow flick, starring Seth Rogen as the harried new college graduate, trying to carve his way in the world while dealing with his meddling, overbearing parents, played by Liam Neeson and Tina Fey.