You know, most people jump straight to the whole 'Naruto with godlike powers' angle with that premise, but I've always found the more interesting fics dig into the psychological weight instead. Like, suddenly his whole life narrative isn't 'the underdog orphan' anymore—it's about being the heir to the literal source of all chakra, the root of the world's problems. That flips his self-perception on its head. Does being Kaguya's son make him inherently a threat, a god, or just a really unlucky guy with terrible relatives? I've seen some stories play it as this crushing legacy he has to hide from the village, terrified they'll see him as the ultimate jinchuriki, a vessel for something far worse than Kurama.
Other takes explore the messed-up family dynamics directly. Instead of finding a cool, powerful grandma, he's got a mother who's a cosmic-level threat sealed away, and brothers like Hagoromo and Hamura who are more like mythological figures than uncles. It creates this weird tension where the 'found family' theme of the original series—Iruka, Kakashi, Team 7—bumps against a biological legacy that's actively dangerous. Does he feel obligated to 'fix' his family's mistakes? Does he resent them for leaving him alone in a world their conflicts shaped? I read one fic where adult Naruto, as Hokage, had to grapple with approving research into the Ōtsutsuki threat, knowing he's essentially signing off on intel about his own ancestral line. That stuff hits harder than another power-up story.
The legacy also reframes his relationship with Boruto. In canon, Boruto rebels against the 'Hokage's son' shadow. But if Naruto is Kaguya's son, then Boruto's legacy is doubly terrifying—the weight of the Hokage hat AND the bloodline of a celestial being. Some fanfictions make Boruto the first person Naruto confesses the truth to, turning the 'passing down the Will of Fire' into a much more complicated conversation about inheriting a potentially destructive legacy and choosing what to do with it. It's less about flashy fights and more about asking if you can ever truly escape where you come from, even if you're Naruto Uzumaki.