I totally support the idea of a 'skip action sequence' button, or have the game play it out for you, because as narrative becomes more important, developers run the risk of spending lots of time and money on a sequence that a lot of players may not get to.
Somebody else mentioned books, movies, and music, and it's a direction that many games move towards. When reading a book, if you're in a particularly difficult place, you can still 'read through' that chapter, get to the end of it, and then continue the story... I have zoned out through a lot of extended descriptions in certain books: I am sure there is worth to Proust describing a pretty flower over 47 pages, but sometimes there's just so much you can take, yet you still want to read the book. The same with a movie or music: I love Wilco's I am Trying to Break Your Heart, but sometimes I don't want to listen to the 4minute aural orgasm of pots and pans banging together with "WHISKEY TANGO FOXTROT" reverberating in the background. With music, books, and movies, for difficult sections you know that they're going to end eventually and you can get through them to experience what you want to experience.
With games, if you are stuck on an action sequence that, for whatever reason, you can't get through, then why not add that feature to let certain people skip through. It gives developers an incentive to put as much effort into the ending chapters of a game as the beginning chapters, because with many games, developers have to know that a good portion of their players simply won't get far enough into the game to experience all of the hard work.
Ultimately, if you don't like it, don't use it. If you feel the need, use it.