The whole point of a game is to involve the player in a certain activity and with video game it is to try to put the player in a role and try to give the sense of actually doing what it is theAy are doing.
A cut scene is supposed to be a neat little clip wear something is explained or just something funny. Really it is supposed to feel like your taking a break for a moment to just watch something.
A quick time event tries to combine these two into one seamless part of a game. It may seem like something stupid, but I think of it akin to startling moments in movies when you jump a bit. One moment your watching something calmly trying to figure out what is going to happen, then the next you spamming x to try to keep your character alive.
I only find them annoying when you absolutely have to do them in order to progress in the game. I feel that at that point there should be two story paths, one for is you succeed and one for if you fail.