"Responding once it happens" is the key phrase here; when trying to respond to something that's already happening at reaction speed, by the time your response takes place the reaction you're trying to respond to has already occurred.
That's simply not true. How many examples do you need?
OK, then, how do you make it so the last person to act (i.e. in the metagame, the last player to declare their reaction) doesn't always win?
Three things here.
First, I don't worry about someone getting a win. A reaction and the spell slot are the player's resource to use, and I let them decide how they use it. It's an expected part of the game, and so I let it play out as expected.
Second, an instance of a counterspell being counterspelled isn't all that common. Nor is it all that big a deal. If one spell going off instead of being countered is that big a deal, then I have other things to worry about.
Third, I try to create situations where reactions matter. Where deciding to use it on one thing means it won't be available for another. This way there are potential consequences for the player's decision. It's definitely not always possible, in which case, I rely on points 1 and 2 to do most of the work here.
When initative rules don't apply (as is the case with chain reactions) the choice is that one can rule things happen in FIFO or LIFO order. LIFO gives too much advantage to the last player to speak up, and FIFO also makes more logical sense in the fiction.
I don't agree with this. The initiative order determines who goes when, it's not about who speaks up first.
Also, what makes sense in the fiction should be what happens. In my opinion, you are creating the problem by wanting the fiction to match the turn order of the game. Which is odd because you're making the gamist element paramount in the fiction, which goes against what you say below:
Yep. When one is trying to present the fictional world as a place where the characters actually live and breathe, gamist concerns all too often get in the way. Sure, there's places where those concerns are valid and can't be avoided; but there's many instances where there's a clear choice between the gamist option and the realistic option, and I try to take the realistic option where possible.
I would think that not adhering so strictly to the turn order when it comes to the fiction... accepting that the turn order may limit and restrict the players more than it does the characters... would pretty much resolve the problem you have.