Certain elements of German culture did not just develop in the last 150-200 years :)
I also read it at age 6 or so.
Many American parents would find it inappropriate for kids given how graphic and negative it is. I think it is a classic however.
The burnt alive story was not about punishment. It was about what could happen if you play with matches. Fire doesn't care how old you are.
As for the tailor, even I at 6 or 7 knew that wasn't going to happen. I didn't know any kids who were missing thumbs!
One of the things I like about the Heute Show is that the gags often point at some cultural thing I knew nothing about (in fact, I think it was one of those gags that led me to reading Stuwwelpeter in the first place). Similarly, I encountered something last week that prompted me to read Max und Moritz. So I assume these things still have cultural relevance, even if as a sort of short-hand, but I certainly see your point (edit: at least superficially).
https://en.wikipedia.org/wiki/List_of_international_game_sho...
Sitcoms also get adapted pretty often. Talk and panel shows, sometimes.
We do the same thing in the US, just a bit less because we've got a really, really big domestic entertainment industry, so something's got to seem just right (in terms of "will this make money?") to get picked up, shouldering its way past all the US-original shows trying to get made, but it does happen. The Office, Power Rangers (half import, half adaptation), Iron Chef, Ninja Warrior (also has a German version!) and a bunch of others.
I'd wager that kids in Germany today (or for the last 40 years or so) can relate more to Tom Sawyer and Huckleberry Finn than to Struwwelpeter, not the least because the former was made into a (quite well done) t.v. show dubbed and broadcast in Germany.