I have the impression that in a lot of the Azkaban fics, the 'power' is something only Harry could have picked up, whether because of his line of descent or because of his connection to Voldemort (and the magics associated with that, including his mother's protections) or because of his unique magical status - which can range from "unusually powerful in some way" to "divinely chosen by magic itself", through a lot of variations on the way. And in a few cases I believe he simply made friends with the Dementors, which is mind-boggling enough (and implausible enough) on its own.
The Naruto idea is a nice one.
The Naruto idea is a nice one.