There is a current 'trend' going on in recent years when it comes to "modern**" vs 'Traditional**' film making.
To fix up your confusion though, Jackie Chan, many other martial artists, or non M.A. people like Tom Cruise.
Do their own stunts because of many reasons. Tom probably uses it as a way to brag, considering his stature, age and popularity, while others do it because they want to shine on screen. Though without asking them directly, or finding some quotes somewhere, it's hard to know why they have to do their own stunts
These reasons are different than mentioning the lack of use of CGI...
Many movie goers, and critics alike have been complaining and generally annoyed with the very heavy use of CGI in the last half decade to decade. It often ends up producing things like the uncanny valley, lazy film directing (fix it in post!!!), when CGI is done poorly it doesn't hold up over the years.
Like I mentioned in the post of "Does Disney no longer produce hand-drawn cartoon films"
There are great benefits to using CGI or sharing practical with CGI. There are great cost benefits, monsters (or moving parts of them) and things are easier to realise than building gigantic sets or weird animatronics for a single 3 second scene, actual environmental and waste savings.
But as said, there are negatives. I'm not impressed by giant crazy 80000000 star ships battles anymore. Anything in my wildest dreams can be made with computers now, they don't look real, there is no real emotion coming from such things, and the actors have a hell of a time trying to act against green screen monsters and backdrops.
Although, I might consider myself an armchair movie snob and perhaps not the majority, the general public isn't impressed anymore either.
So like many other trends, studios have recognised that the average movie goer wants to see real effects again. People want to see actual actors act. with real creatures, real sets, 'real stunts'. Because of this, it's now used in marketing.
"Look at our movie!!!, We use real actors and real backdrops!, We're not lazy using shitty CGI!! We're giving you what you want!!" Well maybe not quite word for word like that...but you get the idea.
These things are important enough that you can increase the box office returns by non zero sum. And while it took more time and effort...it pays off.
I will admit though, there are really great uses of CGI, in a mixed kind of product, like the Dark Crystal Prequel, or even in normal movies. But I welcome this trend of the 'return to practical'.
**Traditional in this sense meaning, practical effects, real actors, real sets, etc, very little computer aided film making.
**Modern in the sense being, very heavy use of computer aided film making, as little as possible left to anything practical.