I think it depends on the game entirely. If you believe it won't detract from the experience that you can skip combat altogether, then there is nothing wrong with implementing it in my opinion. I think games at their core should focus on interactivity, whether it's pretzel moves or just choosing between Option A and Option B.
The developer of Cthulhu Saves the World asked on his Twitter whether a game was really a game if you could get the exact same experience watching a Let's Play (this was referring to Dear Esther). I don't really think that CAN happen, as even pressing forward to move and looking around the environment is more interaction than a movie. Heck, it's completely different to play a visual novel game on your own and watch a playthrough, because the interaction isn't in pressing buttons through menus, but making the choices YOU want.
What I'm trying to get at is, if you make your game such that people want to skip a certain aspect, you have either 1) failed in implementing that certain aspect; 2) the people who are complaining aren't really people who ever liked that aspect. You can skip cutscenes, you can mute music and play your own, you can usually remove excessive gore, you can turn on the lights and speakers while playing Amnesia... There are ways games are MEANT to be played, but if someone bought the product, they should be able to enjoy it on their terms. I don't know if there are people like this, but if you were to read all books by reading the last chapter first and then deciding whether you wanted to enjoy it, nobody is stopping you, but it's missing the point and would make your opinion on said product less valid.
I haven't played L.A. Noire, so not going to comment on how it was implemented there, but let's take a look at Heavy Rain. The game only saved between scenes, and it didn't prompt you, it autosaved, so you would think that the death of a character had weight. Now, this is also impractical, since your gamepad could die, your power could die, your phone could ring and a ton of other things. Yet, that design decision contributed to the game's atmosphere.
But again, as many have said, it's on a game-by-game basis. If you think it can work without detracting from the experience, by all means, go ahead. I'm not gonna whine over how someone else is enjoying a particular game.