In Tim Burton’s film Ed Wood, the gloriously talentless titular director of Plan 9 from Outer Space meets Orson Welles, his polar opposite in ability. Welles was the ultimate “auteur”, a film-maker who imposed a singular vision through all his productions. Is Burton too an auteur, as the Design Museum’s director has it, and as this efficiently kooky show takes for granted? If he is, then he has by now turned the gothic into a brand, projecting such a sharply stylised, recognisable version of homely horror that he can imprint it on almost any material and deliver the outlandish as bankable.

This exhibition is a world touring event originally devised by Burton’s “in-house curatorial team” that is making its final stop at the Design Museum in London. That accounts for the easily packed-up look of it all. It also accounts for its soft-centred, PR feel. It doesn’t ask tough questions, such as how Burton works with technical crews and actors; or, more painfully, why his later output has been so uneven.

Burton was not born, we learn, in a cobweb-covered gothic castle on the edge of town but in Burbank, California. It was apparently a suburban hell. This is made clear in the show’s first space, where his early drawings, ranging from an anti-litter poster to experiments in horror, are hung on a stage set made of identical suburban house fronts. In case of confusion, Burton is on screen in an old South Bank show explaining how he rebelled against Burbank’s sameness and sterility. A wall text is headlined “Surviving Burbank” yet we get no details of why he found the place so insufferable, or what his home was like.

Other youthful drawings show him already fascinated by Halloween and its denizens, portraying comedy monsters at their seasonal feast in cartoons that owe a lot to Edward Gorey and Charles Addams. Horror memorabilia on display includes a beautiful art nouveau edition of Edgar Allan Poe’s The Raven and a poster for the (very) cult film The Oblong Box, starring Vincent Price and Christopher Lee.

This passion bore fruit in Burton’s animated, 1982, black-and-white short film Vincent, showing here in its entirety, in which an American boy refuses to be all-American. He wants instead to be Vincent Price. A poem in voiceover, written by Burton, tells the blackly comic tale. It’s a manifesto for an alternative American tradition, the gothic decadence of Price and Poe. The voiceover is by Price himself.

Puppets of patched and sutured Sally, oogie boogie men, fiendish scientists and Jack Skellington show how, in his early features, Burton remained true to this alternative American gothic ideal. In a glass case, you meet Johnny Depp’s leather suit from Edward Scissorhands complete with those very scissorhands.

Burton really did have a coherently subversive vision of the US in the 1980s and 90s. Edward Scissorhands creates a new American myth, from the samey plastic town where everyone aspires to fit in, to the spooky castle on the hill. Where would you rather live? And do you identify with the ghastly parents in the original 1988 Beetlejuice – or their goth daughter?

This version of the gothic is, as Burton knows, as American as a pumpkin. Poe Americanised horror stories, turning away from ghosts towards decadence as characters improvise eerie violin tunes while their old houses fall around them. Looking at the Scissorhands costume, you realise how elegantly Burton made Poe’s dark romanticism into a new bohemian model – and a commercial hit.

There’s a clip here of the young Burton working as a Disney artist. He gazes blearily at the camera from hollow eyes as he drapes a long thin hand over a chair – for all the world a goth. It was for his drawings that he was employed by Disney. He still does detailed sketches, cartoons and paintings for his films. They are integral to the way Burton the auteur works, including his designs for the unmade projects Superman Lives and Pirates. But as art on a wall, these drawings don’t make it. The sub-Goreyesque style, with a dash of Dr Seuss, that he perfected in his teens apparently still satisfies him. It doesn’t satisfy me. The mediocrity of his pictorial style is obvious when he takes on stories previously illustrated by truly original artists. His drawings for Charlie and the Chocolate Factory are feeble compared with Quentin Blake’s. And don’t get me started on Burton v John Tenniel as illustrators of Alice.

Then again, those two finished films are not up to much either. As you move on to cases full of costumes and props from various Burton “classics”, you see how his intense early imagination turned into a kind of showy display of “imagination”. Michelle Pfeiffer’s Catwoman costume without her in it falls flat, although the snarling Martians from Mars Attacks! still have it.

But how did a lover of American gothic make a film as cynical as Sleepy Hollow, which tramples all over Washington Irving’s 1820 ghost story? And would a true horror fan think Price acted in Hammer films, as two wall texts claim here?

The exhibition, like Burton’s original genius, dissipates in a patchy series of partial returns to form: Miss Peregrine’s Home for Peculiar Children, Wednesday and side projects presented here as high art, such as his videos for the Killers and fashion shoots for Vogue. This is a fun enough show for Halloween, but you will have forgotten it by Christmas.

• At the Design Museum, London, from 25 October to 21 April.