I think that the core problem is that developing good combat (and I know that there are plenty of non-combat QTEs, but I'm reasonably sure they make up the majority) requires limitations. You can do this, you can't do that. If you're almighty, what's the point?
But those constructive limitations are destructive to more traditional story telling, which requires stuff like specific camera angles and, well, variation in activities. Sure, you could come up with a set of more-or-less one off mechanics for a specific scene, like a set of melee controls for when you character loses their weapon in an FPS and is forced to struggle with an attacker to get it back, but not only is that wasteful in terms of resources, it's also difficult to get right enough to avoid running into water level syndrome, where a sudden gameplay change pisses off your playerbase. QTEs are a comfortable middlepoint.
That said, there is a problem with QTEs, namely: overuse. Not every sequence requires player input (press F to pay your respects!). It's okay, we're used to cutscenes.
