There must be.
Haven’t read it, yet, but I have high hopes for the Earthsea books.
Discworld would be a good example of fantasy that doesn’t follow this trope (pretty sure in that world anyone can study magic, but like everything else that doesn’t mean everyone is good at it).
As far as I can remember, the main character is just some random son of a smith.
Only just finished the first entry, and this is still the case by the end of that book at least. The main character does have a kind of “raw power” that goes beyond what others have innately, which is a bit exceptional-ising.
It’s hard to pin down, but the tone is more community oriented, and less about this one Special.