Tell me how you can respond to something that has not happened, yet? Either in game or in real life? That is the heart of the argument. That's a hurdle I don't think you can cross.
I'm not smacking down people siding with you. I'm clearly and concisely laying out how I think they might be incorrect in the assumptions they are reaching, specifically on the pieces of the rules that you quoted.
I am thinking about combat. Believe me.
So, your opponent, in combat, wins initative, and you want to PoF him before he can act against you. What's his first act? It's to swing his sword at you. Without your intervetion the act is successful., his AA is greater than your defense, so it's going to leave a mark. Under my guiding principles, there are two reasonable options. Respond with something that mitigates the attack, or respond in such a way as to make it easier for your sodales to help you out. Oh, and by the way, you also get to attack at your own initiative point with whatever normal action you had planned, regardless of the outcome here.
First option, mitigate the result. The result is you're hit. Your choices are a spell that makes the sword swing away, or leap somewhere out of range. Both options cause the sword to miss, and then you continue with your already stated action, if it's still possible, or pick a new different option, if you've moved out of range. It still happens.
Second option, mutually assured desruction. You're going to get hit, and it's bad, but you can hit him worse. You can fast cast 2 PoFs at him at the point he hits you, and you can also manage to get off 2 more at your normal intiative point (penalties would apply to casting, though, unless the attack on you was a killing blow, then I'd handwave that it's a last stand of a hero, and no penalties apply). You cannot kill him before he hits you, because your first PoFs go off at the point where the sword hits you (his actiion is coincidental to your response). Your PoFs may kill him, or injure him so badly, but you don't know that.
So, you've thrown out some scenarios that you're looking for someone coughing, or presenting some other attack oriented posture and acting at that point. The trouble with that, quite frankly, is that Ars is just not detailed enough to do what you describe, and this is IMO. And even if we adopt the Interrupting Action model, I still stand by my statement: fast casting is a response to an action, and the action is the final result, not the beginning. Paul Atriedes and Gurney Halleck fought each other with shields, and both had killing blows prepared. Could they have chosen to fight differently, drag it out so that only one of them had the killing blow? It's a matter of tactics, that you as a player get to choose. Press on despite the result, or mitigate the result and try and play your advantage for later. Go for the kill, you're taking on the risk that what he does to you won't be as bad as what you do to him. You can't win every battle.
So, if we adopt your model. My NPC swings his sword, at the beginning of the swing, you cast PoF, but his swing lands at his initiative point, but your PoF gets to him before he's finished his swing, and therefore the swing never connects. You want that? Ok...Then my guys can do the same thing. I really don't think you want it. I have other NPC enemies. I've always taken the view that the most dangerous enemies in RPGs are characters most like the PCs. I tend not to use them a lot, but I do have enemies like that, and not just Valerian. I'm vehemently against this for your good, I'm on your side despite you thinking otherwise. I really don't think anyone will like the results of this change, but like I said, if enough people want it, I'm not going to get in the way of it. I'll just use it as you would use it.