First and foremost, i want to want to say in 99.9% of the games that have QTE's, they don't need them.
Secondly, a simply question;
Have you ever played Lost Planet 2? The QTE's are rare, and unexpected, but they actually work well.
They're all cutscene related, but you feel like it's just another part of the game. It's not "press F to pay respects" its "H-H-HOLY SHIT THE TRAINS UNDER ATTACK BY A FUCKING HERD OF UNDEEP, AND IF WE DON'T FIRE UP THE RAIL GUN, WE'RE SCREWED!"
Could they be removed from the game, and it still be fine? Yeah, they could, but that whole games moto was "Kill Big", and when you have a cutscene like that, it just worked out really well. It's one of those (EXTREMLY) rare cases that it works.
But, with Warframe, i don't think OP is talking about QTE's. I think s/he's refering to the machanic like a stealth kill. You have the option to hit melee. Its not really a QTE, at least not to my definition.
Now lets just put that button on the scorpion grapple. If you get grappled, you either ride it out, or tap melee to cut the rope(which everyone will just spam melee to cut it asap). That makes it dangeriously close to a QTE, since the grapple is classified as an animation, but it's still just an option, like the stealth kill.
And then, about the AOE knockdown, all DE would have to do about the knockdown is put in code that says "knockdown+roll=knockdown avoided. Knockdown+no roll=knockdown takes effect".
Now, no, its not that simple, but explainning it that way makes it easy to get.
Have the game sense that the knockdown AOE was cast by the enemy unit, then take into acount whether the player rolled/didnt roll. If they rolled, the AOE would have no effect. If they didn't roll, then it would play out like normal. Its not a QTE, because it doesn't "force" you to do anything. You either roll from experiance, or you take the hit and get back up.
TL;DR
Its not a QTE, its just another machanic like the stealth kill, or the parry kill. The game takes into acount the state of the player, enemy unit, and applicable effects. If specific requirements are met, the corrosponding action is played out.