We can divide everything into 3 periods of time, which are Before Hong Kong, Hong Kong, and After Hong Kong.
BEFORE HONG KONG
From the 80s on at least, the idea of a good action scene was to have a lot of stuff blow up, to have a few hard-ass quips, some big muscles, big guns, but otherwise not require a lot of technical fighting prowess on the part of the actors. After all, the highest priorities for an actor are that they can act, and that they be good looking. Hoping for them to also be able to do back-flips is a bit much, and there’s only so much you can do with a stunt double.
Now, if they were doing sword fighting, then you’d see a lot of effort put in to training the actors. There’s a whole history of stage and cinema sword swinging that has been developed to be fairly flashy. There isn’t a comparative example for fighting (in the West), except perhaps in things like Slapstick and clowning – which isn’t exactly the sort of effect you want.
HONG KONG
Starting around say 1996, there was somewhat of a discovery of Hong Kong films, in the US. In short order we had Jackie Chan release Super Cop and Rumble in the Bronx, which led to the Rush Hour and Shanghai Noon serieses. Some people found out about John Woo’s films, giving him a large enough name in Hollywood to be invited over to make Face-Off.
This gave the US a taste for flashy hand-to-hand fighting. Via Hong Kong, there was a whole branch of martial arts that had been developed to be flashy and interesting, like stage dueling. A few directors and white actors gave it a go, most notably everyone in Lethal Weapon 4 (which brought Jet Li over to make some films of his own, alongside Jackie Chan), and Mark Whalberg in The Big Hit.
Ang Lee kept the light going on with Crouching Tiger Hidden Dragon, but the desire for real hand-to-hand fighting began to fade and overall the Going Kung Fu thing always looked a bit silly as performed by a bunch of whiteys particularly when you know that in real day life, an American would always grab a gun and shoot the perp. The Bourne Identity was able to replace Kung Fu with much more Western seeming moves, but The Matrix had probably shown that you were still better off (in terms of making a buck) to have flashy special effects than to have actors who could do back-flips. And probably most actors preferred it as well.
POST HONG KONG
The problem, though, is that now audiences know that flashy hand-to-hand fighting is possible and they expect it – but they don’t want to see Kung Fu by white people, the actors don’t want to have to learn how to be martial arts experts, and outside of the one-off work in the Bourne Identity there still isn’t a Western fighting style for stage that’s been developed. It’s easier to create the impression of fancy, flashy fist-fights through quick editing than through any other means.
The only alternative is to go back to the stuff in the 80s where you get heavily muscled men sort of randomly flailing about at each other, and expecting anyone to take it serious – or blowing shit up.