These days they can put the star's face into any stunt:
In movies, yes. I believe it was first done in Jurassic Park
, in the shot where the girl was climbing up into the air vent with the raptor snapping beneath her. But the techniques you list still cost money, and are easier to do in big-budget features than on series television.
A lot of movies these days just dispense of stunt performers altogether and use digital models of the actors in the action scenes, but the animation isn't always convincing. I was struck by a shot in The Hobbit: An Unexpected Journey
, during the big underground fight against the goblins, where the Dwalin character just looked so artificial in his motions as he waved the other dwarves across a bridge or something -- he looked like a video game character, and it was bizarre that they'd use a digital double for such an ordinary motion.
Of course nobody's claiming that you could expect any actor to do all
their own stunts; even Jackie Chan is past the age when he could do that. I've already acknowledged that doubling would still be used for the more difficult or dangerous stunts. Indeed, I'm sure everyone else involved with M:I--GP would've preferred it if Tom Cruise had let a stuntman climb the Burj Khalifa instead of doing it himself. But the point is that it's become increasingly common for actors to train to do many
of their own stunts, even the majority of them. Kevin Sorbo was doubled a lot less in Hercules
than Shatner was in TOS.