I appreciate the martial arts context. I share it, albeit in a different art. For our part, we spend varying amounts of time talking about concept/principle pieces of the puzzle, and demoing/drilling very specific techniques. We need (we think) both.

Over time, the regular drilling makes recognition of context a great deal faster, and the conceptual pieces make improv at that point start to look creative or magical, but it's not - it's just all that drilling, and familiarity, and interconnected understanding in gestalt that enables "creativity".