I am not as familiar with Japanese history as I'd like to be, but I think in power struggles on Japan, it would probably be more often the "outsider" "sponsor" the imperial claimant (to be a puppet figurehead) rather than the other way round.
Actions such as the Jinshin no ran of 672 were one member of the imperial line against another, never an outsider acting without the sponsorship of an imperial claimant.
On the bloodline of Amaterasu, as successions had been done via female lines, powerful clans obtained or maintained legitimacy as de facto rulers through arranging marriages with the imperial clan, and voila, effectively placing their own descendants into the thrones. The 5 Houses of Fujiwara clan were most famous for monopolising the pool of brides of the Tenno.
As the imperial clan did not have an official surname or dynastic name, it was easier to maintain the impression of unbroken Yamato lineage of the Tenno.