First off, I'll define both tropes to make sure we're all on the same page. The "Exiled Prince" trope involves an exiled prince growing up away from his kingdoms, having some adventures gaining support from people on the margins of said kingdom, then coming back to conquer it, vanquishing the present king (often either his father or his father's usurpator). Very common in mythologies (Zeus vs Chronos, Oedipus, Beowulf...), present in more recent works like Hamlet, or even more recently, The Lion King , the Legend of Prince Arslan or The Northman. Of course, Aragorn's backstory in The Lord of The Rings takes elements from this, being very inspired by Beowulf, and so does Star Wars, altho without ticking all the boxes. Interestingly, tales of legendary kings who may or may not have existed, or at least were claimed by existing rulers as their ancestors, also had stories of this kind : Soudjata Keita, King Arthur... There's also a fragmentary legend saying Sargon of Akkad's father wanted to kill him because of a prophecy, was stopped by Ishtar and then sent to another guy who was supposed to kill him... then the tablet is broken, but seems like the starting point of many exiled prince stories. This stories indeed seem useful for legitimizing a dynesty: Claiming ancestry from glorified past dynasty, while explaning the dynastic gap, shunning the latest ruler as a villain and justifying his murder, and giving a good role to surround peoples who tale part in this legend as supporters of the hero, justifying their integration in the kindgom.

Now, the "dancing with the smurf" tropes, I'm calling it that in reference to the South Park episode that jokes on the similarities between the plot of Avatar and that of "Dancing with the Wolves". Both movies feature a " white saviour", who comes to a new land/world as a colonizer but "goes native" ends up a leader of the native's resistence. It's also the plot of Pocahontas, Atlantis, the Road to El Dorado...

There's an interesting parallel between these two clichés: They involve a man (or more rarely a woman) away from home finding new allies, fighting the power in place and ending in a position of power, justified by their diplomatic skills and their righteous and victorious struggle against the evil ones in power. There are even some intermediate case that can fit both cathegories, like Dune, or the major part of Daenerys's arc in Game of Thrones.

Now, if the exiled prince trope was so useful for its ability to legitimize a dynasty's rule over a set of people, does the "Dancing With The Smurf" trope owe its own to the way it reassures people living on settler colonies that they deserve their place there, as lkng as they don't support the most evil parts of colonialism?