I was mixing microphones for a school tour yesterday, and I realized I was, once again, not just mixing for that moment of that song, but mixing in context; of the whole song, of the total performance.
I'm reminded of a couple of classics of science fiction when I think about this. In Robert Heinlein's "Blowups Happen" the staff at a power reactor are going insane from the tension of the job. This was written before the operations of the first pile became publicly known, and Heinlein had extrapolated a fission reaction in positive feedback; balanced on the cusp between dying out or going into runaway (what the industry now calls a "power excursion."
His people, experienced nuclear physicists all, were forced to monitor the processes inside the massive power reactor second by second, using calculus to project the widely varying curves to decide when to moderate -- knowing if they slipped a decimal, a massive explosion would take out half a continent.
The stakes are similar in SF Pioneer E.E. "Doc" Smith's The Vortex Blasters. In this case, the (seemingly) natural phenomenon of a loose atomic vortex behaves chaotically. At any given moment, you can take the past few minutes of activity and attempt a best-fit curve. And if you could do this well enough, you could time a large explosive charge to arrive at the core of the vortex at the exact moment that the yield matched the energetic output of the vortex, thus snuffing it out like an oil rig fire.
Enter "Storm" Cloud, physicist and lightning calculator, who did this personally using his ability to perform complex calculations in his head (eventually he is replaced by a specialized computer...but the real solution to the loose atomic vortices and the source of the problem is more interesting than that. The story stands up well -- still worth a read today).
Fortunately mixing a show is much smaller stakes. But that doesn't change the problem. Given an ideal audio space, ideal sources, perfect equipment, and no psychoacoustic or physiological auditory limits, you could set up a perfect mix for every moment.
In the real world, you have issues you have to map around. One big one is hearing fatigue. If you want to have the ability to push a powerful musical moment into the peak power you are legally and ethically allowed to deliver to the audience, you need to hold back until that moment. Otherwise the audience will already by fatigued and will be unable to appreciate it. Every show, every act, every song has an internal dynamic arc, and you don't start every song with screaming levels; because that leaves you nowhere to go.
I also look ahead knowing a flute is going to enter and I need to carve sonic space for it now, instead of having its entrance masked by competing material. I mix knowing I have one singer who isn't on microphone and the mix that will work during her solo is not the same as the optimum mix a few bars before that.
And I also have to mix into history. Say I guessed wrong on the EQ for a trumpet and gave them a specific and distinctive flavor. That means I have to make a lightning-fast decision about where to go into total artistic mix. If I change it now, the audience's attention will be attracted to the change instead of to the solo, leading to a poorer experience. On the other hand, when the trumpet entered it was new, and the audience is not burdened by the same preconceptions I (or the musicians) might have about how it is "supposed" to sound. Within that first few seconds, they may accept this as musically valid, and the song will work.
The window to make this choice is only a second or two. And it is a multi-variant problem; the sound might be "slightly" off, but it might be so in a way that will stand out later in the song, but the song itself may permit adjusting before that other moment occurs...
And in the middle of this same window a vocalist may have decided to shift her position on a mic and need to be fixed now. Which means even less time, and even less brain power to spare on figuring out where the potential fixes may fall within the total context of the moment, the song, the act, the night. And, yes, I do slip. I have someone suddenly sound utterly wrong, and as I'm fixing that, I blow an entrance.