But the thing is that it's not. The outer "Japaneseness" of the whole affair is only briefly convincing. As an instructive comparison, let's look briefly at Princess Mononoke, another of Miyazaki's movies that I would say is truly nativist.
Princess Mononoke is set during the Muromachi period, around the 15th century, about as distant as medieval Sweden in The Seventh Seal. Its plot centers around an exile from an Emishi community in Japan who comes west to find that an industrial iron-mining operation is moving into a forest that's under the protection of a group of territorial spirits, and tries unsuccessfully to find a way to navigate the process without whipping it up into a war. It's a fairly nightmarish movie, in a lot of ways—in the first scene the main character gets himself cursed by a giant boar, the movie ends with a Godzilla-sized monster made of terrifying black goop tramping through a forest, and in between are a lot of lepers, bleeding pigs and massing of squirming black worms festering inside of wounds, the upshot being that the magical elements of the movie are persistently presented as terrifying and unknowable, even when they're not necessarily malevolent. Moreover, a lot of them are physically amorphous—the huge Godzilla monster at the end is an extreme example, obviously, since it's mostly made of black goo, but even the strange little forest spirits that recur throughout the movie have a melted, colloidal look to them.
The effect of all this is that the spirit world in Mononoke is best understood as a kind of force rather than as a cohesive world that truly intersects with our own. It's more of an immanent disordering principle than a separate setting in and of itself. Mononoke's setting—from its local geography to its details—is extremely, intricately, obsessively fleshed out, but the points at which the spirit world intersects with it, things become fuzzy, and the rules don't really apply anymore, or at least become extremely inconsistent. Much of the movie relies on juxtaposing the human need to impose order on nature with nature's ultimate, uncontrollable irrationality. It's a conceit as old as history that Mononoke repeats enthusiastically.
Spirited Away, on the other hand, inverts this formula. It's set in a vision of modern Japan, a country of infrastructure, highways, and a national economy, which collides with an idiosyncratic vision of a spirit world that isn't immanent in our own but highly segregated, and isn't a disordering principle but a highly ordered one. Our heroine, a girl named Chihiro, stumbles with her parents into an abandoned amusement park (built, her father informs us, during the boom economy of the 1980s, and quickly closed once the recession of the 90s hit) and, from there, into a strange otherworld, in which she worms her way into a job at a bathhouse for the spirits.
Through the entire world-building of the movie, it neatly flips around Mononoke's spirit/human dichotomy: what little we see of the world outside the bathhouse, in the first fifteen minutes of the movie, is an amorphous mass of highway interchanges and houses that flow by outside the window; it's not so much a distinct place as a backdrop, and contrary to Miyazaki's usual obsession with detail, it's absolutely indistinct. There's no way to navigate it; it's an anonymous Potemkin village, seen completely in transit. More than anything in Miyazaki's work, it resembles Ozu's depiction of Tokyo in Tokyo Story in its total anonymity: the infrastructure of contemporary Japan makes it impossible to navigate the outside world as a coherent geographical space, and it becomes more like a subway tunnel, connecting space to space without any real spatial existence of its own. In this way it's as immanent yet indistinct as the spirit world in Mononoke.
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When we look back at Mononoke, we see that it's set in a medieval past so distant that's it hard to distinguish from fantasy in some ways; communities are totally insular, with no question of infrastructural connection or even necessarily of linguistic compatibility, and the movie hinges around the rampant tribalism and outsider status that this engenders. The main character's Emishi heritage makes him an outsider from the iron-mining community he encounters; the iron miners in turn define themselves as separate from the spirits in the forest. The factional conflict that this creates is worthy of Starcraft.
Tribal borders in Spirited Away, as it were, are far hazier. It's true that when Chihiro first enters the spirit world, she's clearly marked as a human and has to hide from spirits who might hurt her if they knew. However, there's already a bureaucratic solution in place to her problem; all she has to do is make her case to the owner of the bathhouse and sign a contract, and she's immediately accepted as a member of the workforce. This kind of slippage between the human and spirit worlds would be almost unthinkable in Princess Mononoke's world of rigid tribal boundaries, in which the girl-raised-as-a-wolf character of San is exceptional precisely because there's no template for her. Where San functions as a red flag on the tribal boundaries that drive the narrative in the movie, Chihiro's status is unusual but fully precedented.
This kind of easy slippage between cultural identities extends all the way to the mise-en-scene. In the scene in which the spirits are first introduced, they disembark from a Mississippi River steam ferry and process through a town full of tacky neon lights, many of which say "CafĂ©" in the Roman alphabet, while an Okinawan (not Japanese) shamisen plays in the background. The owner of the bathhouse lives in an elaborate apartment with European decor and wears Victorian dresses. Nobody ever remarks on any of this. Miyazaki seems to be presenting a world in which a huge number of cultural and social influences coexist more or less peacefully—albeit not without corruption—and that's a far cry from Mononoke, which effectively centers around a race war.
If you accept the thesis that the spirit world is an abstract manifestation of Japan's cultural psyche (which is itself a pretty big assumption that I'll leapfrog right over, but if you'd like further reading there's a chapter in Susan Napier's book on anime about that phenomenon) and that the bathhouse is a place where that psyche can be literally purified, then it's telling that Miyazaki goes to such trouble to make it both global and functional. It would be pretty facile to conclude by saying that Miyazaki's rejection of the simplistic antimodern predilections of earlier Japanese films means that he's evolved as a writer past his easy condemnations of tribalism in Mononoke, so I'll just add that if there's any pop culture phenomenon that better embodies the twenty-first century than Spirited Away, a movie that casts a sympathetic eye on the possibilities of pluralist society, using a medium that was appropriated from the west and is now being re-imported as an important Japanese art form, I can't imagine what it is.