Many folk/fairy tales are universal. Some, like CINDERELLA and BEAUTY AND THE BEAST come down to us from the ancient Greek Myth CUPID AND PSYCHE ( which was split in two, for those named fairy tales ) and were originally tales told by and to adults. They were then sort of cleaned up and told to children, getting more and more sanitized as years passed.
Historically, many women died in childbirth, husbands remarried, so step mothers were much more of a norm, than they are today. And these stepmothers often cared much more for their own biological children than the step ones.
Famines and plagues were also common, so there are some fact based, though by now clouded versions of what happened at those times,
Tales of adoptive parents also are included in some fairy tales, as are childless couples, because there was NO medical for the barren back then.
Most children can hear the less cleaned up/more gory versions without having nightmares/being scared, than adults might care to believe; though the sexual overtones in some of them ( SLEEPING BEAUTY ), should be left out!
And all of them, like Aesop's Fables, do teach lessons that children need to learn.
A few of those are a bit risque as well but they are also good lesson stories.