It does, though. The Vault boy, Pip-boy, power armor, Brotherhood; it's the trademark of a Fallout series, and all of it is uniquely American in lore. Fallout revolves around Vault-Tec and the Vaults, and without it the world in 2280 would not exist. It just simply would not work in China under the Fallout brand without an enormous breach in lore, unless it was specifically about the American invasion (and even then, it would only really work as a DLC). Leaving America just tosses virtually every facet of Fallout into the trash. It may as well be post-apocalyptic game #26781 without those vital Fallout aspects.
American consumerism and the parody thereof is a central theme, at least in the three most recent games. Vault-Tec in general, Nuka-Cola, most of the companies seen, Liberty Prime, et cetera; all of it is a parody, mockery or sarcastic quip about 50s (and occasionally modern) America and American culture. It may not be important to you, but for me it sets Fallout apart from the teeming hordes of post-apocalyptic "games" that saturate the games market nowadays.
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