I think it's an issue of "inside the box" vs "open-ended" fields, that we don't have really good vocabulary to talk about. 'Katas' work great for sports that are very much inside the box. You can innovate new strategies, but the rules of the sport set up an unchanging microworld that you must stay inside of. Coincidentally, these are also areas where even current-day AIs often dominate. Established scientific disciplines with research programs are sort of half and half. You can train people in them, but they can also benefit from serious paradigm shifts and there aren't any a priori hard and fast rules about things that absolutely can't be done, like the rules of chess for the chess-playing domain.
Then there's proto-science when things haven't coalesced into a discipline yet, philosophy when it hasn't been professionalized to death, Kegan's stage 5. This is raw pattern matching, flashes of insight, original seeing, very open ended exploration of an unknown landscape. I don't think anyone has had much of an idea for how to systematically train people for this. This place is also where a lot of the actually efficient rationality practice lives.