I've always had a minor interest on Goth culture, despite not adopting it myself. I wasn't aware until watching "Beetlejuice" that Goths were around as far back as the 1980s, and the niche culture apparently started in England around that time.
I was under the mistaken impression that it really took off in the early 2000s, but that was just when it became mainstream, and communication of ideas (including Goth culture) became more widespread and faster.
What I found interesting was reading blogs by people who called themselves "elder goths," and I looked at pictures of them, but they didn't look old to me. It was very puzzling. Had to do some research and found out that apparently the Goth thing was originally considered a "teenage phase," but not everyone gave it up after reaching age 20, and within their sphere, they apparently consider anyone over 40 that still wears Goth clothes and still enjoys the culture to be an "elder" among them.
And Tim Burton is definitely the textbook definition of a Goth. No surprise his most popular films appeal to such a group, as well as many other people.
Goths emerged from post-punk in the late-70s and early 80s. Bauhaus, The Banshees, The Birthday Party, The Cure, all of that. The subculture was particularly focused around northern English cities back then, most especially Leeds -- which, I think, was home to the world's first goth nightclub. Even to this very day, if you want to see a good, old-fashioned, proper Goth in the wild, Leeds is probably your best bet in the UK -- although, sadly, it's now vanishingly rare to find a young woman dressed in a dyed wedding gown drinking cider and black in the corner of a dingy pub. Times have changed.
Burton is clearly a bit of an old goth in his own way, but it's much the same as any other youth subculture: it gets commercialised, monetised and thereby sanitised. For Burton, it's more about a quirky/spooky aesthetic rather than a rebellion or rejection of societal norms. He's generally thought of as Goths' favourite film maker, but that's only really because it's either him or FW Murnau. The man works frequently for the friggin' Walt Disney Company for crying out loud. That's about as Goth as painting your nails black. Big whoop.
I think one reason his most famous films appeal to so many Goths is because it portrays the main characters in a way that many Goths feel in mainstream society (though you don't actually need to be a Goth to feel that way at times). Awkward, outsider, weird, bizarre, dark, romantic, misunderstood. Several of the stories show wish fulfillment where the awkward, dark, weird character finds love and are accepted by the community, but sometimes with a bitter-sweetness at the end. Plus, he has that unique, interesting, weird, dark but not evil, twisted aesthetic in his movies that few other films have tried and succeeded at.
To be fair, his "Nightmare Before Christmas" thing wasn't originally Disney. They bought the story from him, he bought it back, and it slowly came to become a cult favorite and is now marketed as much as Baby Yoda.
Eh. It's all a bit Goth Lite, if you ask me. It's like Pepsi bringing out a Bible Black edition.
But I nevertheless think you're right about the appeal... and also the fact that you don't need to be / have been a Goth to feel that way (like a misunderstood outsider to mainstream culture). A lot of people do at some stage in their lives even if they've just passed through that as a phase. The Goth thing is just one of the many expressions of that feeling... which probably explains Burton's wider appeal too. Many people can relate to those themes.
Plus he came up with some very original stories. I mean, how many people do you know have come up with such weird ways to interpret the afterlife, a ghost who made a living out of scaring living people out of houses, or holidays turned on their heads, or even Frankenstein-like creatures with scissors for hands?
Excellent post, though I would note that Burton is done with Disney. He has stated that he no longer wants to work for the company because it has become so different than what he originally experienced.