I think most people's problem with QTEs is that they are done poorly. Uncharted is a great example, there being like 2 in the entire game at completely random times.
However, as others have said, they can be an excellent manner of allowing the player to engage in more visually-impressive and (for lack of a better word) cinematic actions, that just aren't possible in regular gameplay.
If you look at, for example, God of War, there are lots of moves and abilities that Kratos has in his arsenal during gameplay, but most players will eventually kind of stick to a small handful of them for their gameplay. And even if you don't, there isn't much that's visually different from kill-to-kill, even when using different moves. Kratos may move differently, but the enemies just seem to take a thousands cuts and then fall over. The QTEs in God of War allowed you to interact with the enemies more closely and perform a much most impressive kill (unfortunately it was let down by always being the same event for the same enemy, which got just as samey as the regular gameplay in the long run).
The point is, in most games' standard gameplay, you can't run up, knock an enemy in the air, cut him 10 times with a sword, grab him around the neck and throw him to the ground again. And if you can, it usually doesn't look very impressive. But in a cutscene, the character can do all sorts of impressive things, and I thin QTEs are a good method of allowing that to happen without robbing the player of being involved in it (as Yahtzee mentioned in one of the DMC videos).
Obviously, though, they need to be done properly. They have to be a core part of the gameplay, not just thrown in from time to time. They also, in my opinion, need to be less "random button flashes up and you hit it" and get to a formula where individual buttons correspond to a general category of actions. For example, in the Shenmue QTEs, when an A button flashed up on the screen, the action that resulted from it always resulted in a "leg/kick based event" in the cutscene, while X corresponded to "hand/punch events" and directional buttons usually meant the character moving in that direction in some what. Lastly, another lesson from Shenmue, they shouldn't be instant fail. You could usually fail one or two QTEs in a given cutscene and still succeed in the end, and in some cases, failing a QTE segment didn't mean failing the game, it meant you had to find a new way to do what you were trying to do.
However, as others have said, they can be an excellent manner of allowing the player to engage in more visually-impressive and (for lack of a better word) cinematic actions, that just aren't possible in regular gameplay.
If you look at, for example, God of War, there are lots of moves and abilities that Kratos has in his arsenal during gameplay, but most players will eventually kind of stick to a small handful of them for their gameplay. And even if you don't, there isn't much that's visually different from kill-to-kill, even when using different moves. Kratos may move differently, but the enemies just seem to take a thousands cuts and then fall over. The QTEs in God of War allowed you to interact with the enemies more closely and perform a much most impressive kill (unfortunately it was let down by always being the same event for the same enemy, which got just as samey as the regular gameplay in the long run).
The point is, in most games' standard gameplay, you can't run up, knock an enemy in the air, cut him 10 times with a sword, grab him around the neck and throw him to the ground again. And if you can, it usually doesn't look very impressive. But in a cutscene, the character can do all sorts of impressive things, and I thin QTEs are a good method of allowing that to happen without robbing the player of being involved in it (as Yahtzee mentioned in one of the DMC videos).
Obviously, though, they need to be done properly. They have to be a core part of the gameplay, not just thrown in from time to time. They also, in my opinion, need to be less "random button flashes up and you hit it" and get to a formula where individual buttons correspond to a general category of actions. For example, in the Shenmue QTEs, when an A button flashed up on the screen, the action that resulted from it always resulted in a "leg/kick based event" in the cutscene, while X corresponded to "hand/punch events" and directional buttons usually meant the character moving in that direction in some what. Lastly, another lesson from Shenmue, they shouldn't be instant fail. You could usually fail one or two QTEs in a given cutscene and still succeed in the end, and in some cases, failing a QTE segment didn't mean failing the game, it meant you had to find a new way to do what you were trying to do.