I think you've simply redefined genius. Many years ago I read an article on youth football, if I remember correctly, and in it there was a bit about the writers visit to the Ajax Youth Academy. In it he writes of a moment during practice when a plane flies over and all the 7(?) year olds on the pitch look up to see it except for one kid who keeps his eyes on the ball. That kid (of course) grows up to be a very good midfielder for Real (I'm forgetting the exact details, I think its Wesley Sniejder?). My point is: whatever that motive energy is that manifests as the single minded pre-occupation with math at an age when everybody else's attention is all over the place is that inherent thing that people call genius. I have read many of Thurston's non-mathematical writings about himself and in it this sort of singular pre-occupation is also clear -- which is why he developed his preternatural geometric vision.

Indeed, it does involve redefining genius as a "state", or "flow", or "trajectory".

When I say it's not primarily genetic, many people wrongly assume there's an entirely explainable and replicable way of accessing this state. There isn't.

The 20,000 hours rule is a bit misleading, because who gets to invest 20,000 hours into something? How do you create this drive, this trajectory? You must have a good hope that it'll yield something worth the effort.

This is why the injunction to "work harder" so often misses the mark.

However, even if only a tiny fraction of the population will end up becoming a "genius", it's very important to debunk the myth, because the real story has valuable lessons for everyone: it gives concrete and pragmatic indications on what one should be on lookout for.

It's not fully teachable up to genius level, but the directionality is teachable and extremely valuable.