I would like to have that as an option in certain games, for example, when I was playing FFXIII, I was enjoying the combat until the last part where it got so frustrating I was about to stop playing, swearing never to try again, in that case, an option to skip certain fights would'be been awesome, since I did end up forcing myself to continue because I was curious about what happened next in the game.
There have been a ton of other games in which a simple section was enough to get me to drop the game and never play it, or search for cheat codes or lower the difficulty, but some games don't offer that option, currently, one of the games I'm playing is Agarest Zero, most of the fights are boring and in other cases, frustrating, also, as far as I know, I can't lower the difficulty, having the option to skip combat in this game would allow me to enjoy the story events without dealing with the combat parts.
So you see, an option like that would be extremely helpful for a section like that, specially since not everyone has the skill and/or time to figure out how to deal with situations like those that I described. Though I agree, having an easy difficulty where it's pretty much impossible to die would also solve that problem, thing is, some games that offer easy difficulty also lock story stuff unless you play on harder difficulties.
Suggesting to look into other mediums if you want to skip the combat is a bit annoying IMO, specially once you consider that, you can't find Agarest Zero in other mediums, you can't get Bioshock in other mediums, basically, games have unique stories and characters and people shouldn't have to miss out on all that stuff just because they may not have the skills to deal with the other aspects of the game.
It wouldn't work with every game, but I do think it should be an option in games that are linear enough to handle an option like that, for other games, just make it so enemies can be killed with ease or make the player an invincible killing machine or something like that.
Basically, everything that's already been said.