I think implementing "obvious intentional styling" is an AI problem. Suppose you copy a header, click in a normal paragraph, and paste. Keep styling information? Case 2: copy styled text from Keynote, and paste. Keep styling?

Maybe, the logic in a word processor should be to keep character styling, but not paragraph styling, but I think there will be many edge cases (for example, the user might be using the word processor as a document layout package)

I doubt those edge cases can be programmed away; user intervention is required. Microsoft solves that after the paste. That may be the better solution.