Done right, I think a QTE can immensely benefit a game. My two favorites, off the top of my head, are God of War 3 and Infamous 2
GOW3:
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Is a twofer. The first is pushing in both analog sticks to gouge out someone's eyes. It is mostly just funny (in that sadistic 00s gaming kind of way...), but it sets the stage for what really matters. Been 13 or so years, but the final fight against Zeus (?) involves you mashing buttons to punch him. Which is pretty normal for the game. But you keep punching. And punching. Until nothing is left but a pile of paste as you keep punching the stone beneath what was left of his skull. And it only ends when you, the player, realize it is over. For all the flaws of the original God of War trilogy, that is one of maybe three or four moments that would be worthy of Teal'c's Kratos.
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And Infamous 2 (and spoilers for 1):
::: spoiler spoiler
I am kind of outspoken for how much I love Infamous 1 and 2. The fact that 1 is all about sacrificing EVERYTHING to be able to stop The Beast, right down to traveling back in time to murder the love of your life so that you won't hesitate when the time comes. And then 2 opens up with you getting the shit kicked out of you and failing with it all being for naught. And the overall themes throughout the game of Cole knowingly destroying himself for a second chance (Half as long, twice as bright). And when the time comes... your heroic ally is terrified because of what she might lose and your villainous ally is right there with you with her understanding that nothing matters outside of stopping The Beast. And it just works so well that Cole drops The Beast like it ain't no thang, just to prove he can, before getting ready to activate The Device that he knows will kill him and possibly all other powered individuals. And the QTE is just to have you slowly, one shoulder at a time, press down all four shoulders of your controller. And it ends with the simple message of "let go" and the knowledge that it is up to the player to put the game down and acknowledge it is over.
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All the "mash these twelve buttons to dodge this boulder" and even a lot of the Yakuza/LAD ones don't do a lot for me. They are more annoyances than not and I tend to streamline them in any game with accessibility options.
But done right? QTEs are some of the most powerful tools in a game developer's arsenal for truly immersing the player and conveying the emotion of a scene.