Intuitive learning for mechanics is extremely hard to do right and you have to know for sure that what you're planning to teach is important. That is pretty difficult when at the end of the day, the community often is the stronger determinant of what techniques are important. Complexity for FGs builds out in an organic fashion, despite the systems themselves being deterministic.
Look at SF3 for example. Did Sean's basketball parry game do anything for you as a player? Did you feel you were better at swatting down projectiles after doing it several times? Did you feel how fun it was(or wasn't) influenced your opinion of parries? I think it's close to a best-case example of how this stuff can work, because doing a parry is simple and the parry mechanic is vital to the game. But if you make the goal just a little more complex, like 'when and when not to parry', it becomes really difficult to represent this through a minigame without it becoming a tutorial.
Can you think of a system that teaches players how to do stuff like OSes or special input shortcuts without the the player having to sit down and think about what they're doing? There's a razor thin line that exposes the entire thing as superficial('a tutorial') when crossed.
I do think it's possible to tie carrots/incentives to learning like some people have mentioned, but making meaningful/meta-learning intuitive is one of those problems that is bigger than the game itself, kinda like making a worthwhile enemy AI.
