The test will go here when I have a post. More examples below.
Why it persists
The trope persists because it solves a real problem cheaply. Fantasy worlds are enormous and the reader needs a reason to care about them. Attaching that world's fate to one person creates stakes instantly. The problem is that stakes and investment are not the same thing. I can understand that the world will end and still not care who saves it.
The writers who solve this — Le Guin, Tolkien at his best, Robin Hobb consistently — solve it by making the chosen one's inner life more interesting than their destiny. The external plot is a container. What fills it is a person who would be worth reading about even in a world with no prophecy, no darkness rising, no sword in any stone. That is the harder thing to write. It is also the only thing worth reading.