Back to the Batman Arkham Asylum example, there's a whole lot of impact when Batman beats the shit out of a guy, far more than any quick time event could give.
Why? In both cases, you're effectively doing the same thing: pressing a button when the game tells you to. The only difference is the presentation, and I guess implicitness versus explicitness.
That's too reductive. During a QTE there can be significant reduction in the sense of control, and consequently of immersion, relative to being outside of one. Part of that I suppose comes from a lack of choice. Outside of an event you're free to play around with whatever the game allows you to do. In a QTE however you're locked down to whatever the game dictates that you do in that particular instance, and rather than perform the actions directly you're just playing Simon Says with the buttons to keep the event (of which your attention is now also not fully towards) from stopping.
Dividing your attention between an abstract minigame and the animations on screen can help break immersion, which would obviously affect the impactfulness of your actions. But that's all in Batman. In God of War the brutality of the quick time events is what's impactful. In Asura's Wrath the presentation of the prompts in tandem with the insanity on screen is what's impactful. But in Batman, I'd say it's the tight controls coupled with the fluidity and brutality of the combat that's impactful. Like cinematics, there's no singular universal rule for these things, nor should there be.
I remember back when the cinematics argument was a big thing. A lot of people against them were saying it was just lazy, a crutch for conveying story when the medium is capable of so much more. Since then there's been a bunch of games with interactive cutscenes, whether with dialogue circles or the whole walk 'n talk thing, or something else, but also still cinematics. The medium is capable of cinematic experiences and your Super Puzzle Platformer games all the same, and there's gonna be an audience for both. Hell, sometimes it'll be the same damn people.
If there's ever too much of a thing, maybe the mainstream shifts gears. If it doesn't, there's surely some corner of the industry that'll have what you need, whether it's an indie or something on kickstarter. But trying to force a shift probably won't get you very far.