I'm confident that the technical skills can almost (e.g. disabilities) always be trained, given sufficient time.
Creativity/inspiration seems to be missing culturally. Consider for example Maths or Physics, where creativity is essential to internalize the material, but the teachings usually emphasize memorizing a few tricks to solve well-known problems and pass the year.
But even if it could be trained, there's 1) the luck factor 2) inborn quality variations. Some people just have it in their bones more than others, even if it manifests "just" as being more relentless in practicing.
That's to say, I mostly agree with you, but I'm curious as to how far we could reach with different teaching approaches.