Honestly, I've never found them to make things more engaging. If I'm interested in the story, having to fumble with the controller during otherwise static periods pulls me out of the narrative (in contrast to just letting me keep playing during these events - that does seem to increase engagement).
My view is that it's theoretically possible to design interesting quicktime event system, but that it tends to mash your verb-space together. In general, you get a stronger message with a clearer relationship between the button the player pressed and the verb in the game.