Interesting analysis. I was going to post a comment about martial arts movies, but the analysis already takes that into account. I wonder if the central focus of guns in action films set in more modern times requires more cuts in order to obtain the most visceral part of a fight. Whereas in martial arts movies you can do a close up of a face to establish the character's emotional state, then zoom out to a full body frame - in both cases you still have a sense of emotional/personal expression. I don't know if you can do that with gunfights, where the individuals are performing a much more limited set of actions.
To which I say, kidding, yes?
The gunfight, tension filled, is the hallmark of the western, the action genre of western cinema. Real gunfights take seconds, less than minutes certainly, they've always been extended so you can cat and mouse it, so you can linger on their faces. Heck, Once Upon a Time in the West is 60% extreme closeup, or some other exorbitant ratio.
That said, the post wanted to talk about fighting more than just action, and non-martial arts (this includes boxing) has typically ignored the skill part, endorsing showing mainly the physicality of fighting (ideally), and sometimes just the effort of it (grunting a lot). Some of this comes from a professional wrestling like obsession with big immovable men in their action stars--so much so it's interesting that they pin point Bruce Willis, the only action star out of the 80's to be built like a fit man, instead of a, well, professional wrestler.
I think it's funny that Bourne Ultimatum is such a high watermark, since that's the Bourne movie that conceded it's shaky cam aesthetic with a capoeria inspired fighter. You don't add that style in film if you aren't conceding to aesthetics, to the appreciation of the body and skill.
I think the piece finished with a very good fight, with Cronenberg's set piece in Eastern Promises. Possibly though, the other true fight on film is the one in Casino Royale, in the bathroom. The graceless but skilled killing of another person, in particular contrast in the most glamorous of movie franchises. If anything, the Bourne movies fetishize the skillful killer more than any other. It disorientates exactly when death is going to be inflicted.