What a weird coincidence, since I actually am doing karate too... And I totally get what you're saying. There is a tremendous amount of knowledge hidden in each kata (in addition to having to remember the kata itself, and there are 26 of them) and without repeating how you describe it there is just now way to make progress in shorter time intervals. But I would not have thought to make the parallel between math and karate, I always viewed them as requiring distinct learning approaches.
That's great! The standard practice advice I give my students (and use myself) is that it is best to practice each of your kata twice each day. The first time you go from Heian Shodan on up, at half speed, just to get it into memory. Then you go in reverse order at normal speed so that you don't get bad muscle memory from always doing it in the same order.
Of course, that's half for exercise instead of just memorization. And obviously it's less necessary from a memory perspective pretty quickly, I can go at least many months without doing a kata and still rapidly pull it back into working memory from a video review (during those times in my life when I couldn't practice regularly) and a few times through myself.
But if it's not in active memory I definitely won't be improving it. Just reinforcing the memory and getting a bit of exercise.
