Struwelpeter is not fairy tales by any definition. It is a hilarious and gruesome picture-book with small moralistic verses intended to teach children good manners. It is an original work, written and illustrated by Heinrich Hoffmann.
Grimms fairy tales are folk tales collected by the brothers Grimm as anthropological research. We don't know the original authors of these stories. It was an orally transmitted genre, and many stories exist in multiple versions. This genre of folktales were not originally intended for children, but at the time of the collection there was a boom in children's literature, and the Grimms cached in on that by publishing modified versions for children.
There are other collections of folktales beside the Grimms, for example the french Charles Perrault. Disneys Cinderella for example is based on the Perrault version, not the Grimm version. I'm not sure what the "English translation" in the article refers to?
Hans Christian Andersen wrote original stories, although to some extent inspired by folktales, they are a very different genre of literature.
While not a fairy tale, the "Max and Moritz"  story by Wilhelm Busch is much in the same vein and to this day a common bed time story for children in German-speaking countries.
I know when my son was young we told him that people smoking were poisoning their bodies, and after that he would get upset and teary eyed when people were smoking because they were hurting themselves.
They don't go to gory details, no point in that, but they don't avoid it either. Times were different - half of kids before age 5 died, everybody could easily die from flu, inflamed appendix or a tooth problem. There were public execution held in bigger villages and towns. Wars, skirmishes and murderous bandits ravaged countries.
Killing of domestic animals was (and in many places still is) a fiesta for whole family, including the smallest, ie butchering of a pig or sheep. Not done somewhere hidden, but in plain sight of everybody.
I don't think we get how exposed to brutality in many forms the kids were back then.
Also, I have modern print of original texts and see no issue with reading them, many parents still read them to their kids. I was exposed to them as a kid and didn't find them shocking.
Deaths in the family used to be pretty common. Lots of children didn't make it to adulthood.
It's a pretty modern idea that we are supposed to survive childhood and live to be like 80 years old and dying sooner than that is all shocking.
It is our modern kids who do not get it.
I read my kids the originals and it works as fine as the disney versions.
When my parents read the story of Paulinchen to me as a kid I immediately understood that she was gone for good. The picture of the pile of ashes and the two cats crying rivers did a good job at conveying what death means.
So called Bush Meat is not uncommon. It's a jungle out there. These tales do have an element of truth. But they are understood as from a different time (nearly the same thing). It's brutal realism. What is disturbing about this?
Showing somebody into an oven pales in comparison to sending them to the salt mines
You just have to take a look at the crying cats extinguishing the ashes of burned-out girl with floods of tears, to realize that this is indeed (very dark) humor. And it has nothing to do with the Grimm fairy tales, except both were published in German. Its like lumping together Beowulf with Charlie and the Chocolate factory because both are in English.
Anyhow, I always loved the great illustrations and stories.
Any fan should also look up "Max und Moritz" in the same vein.
They were all pretty harsh and somehow we never talked about what happened in them.
Just read, good night, lights out.
with limited happy endings and scary artwork. (Try "The Lambton Worm")
I did not like them very much, though, because the moral of the stories is inevitably that if you don't conform, bad things are going to happen to you.
From a German perspective book cancelling (burning) is an incredible dangerous road. We had that in our history once and its lead to nothing good.
Create better ones and advocate them. Disney did that, just, in a bit too American style (oh-my-god-my-kid-cannot-hear-this-word-or-see-a-boob). That is the road.