Does he? It’s been a while since I’ve read the books but my recollection is that he never actually develops a ton of deep skill, or at least it’s never seen. His biggest accomplishment in magical terms seems to be his ability to do the patronus charm at an earlier age than most. Otherwise most of his success comes from 1) bravery, 2) friends, or 3) luck. At the end he chooses to be an auror, which I thought was odd because it seems like he’s poorly equipped to do that job.
It’s true that the books do not paint his journey as instantaneous (except his proficiency flying the broom). But they also don’t really paint his journey as ending in a place of impressive skill.