"I wonder if any game actually constructed a complex polynomial across multiple terms to smoothly scale loads of factors (smoothly as in differentiable and continuous multivariate functions)."
Can you say that in English? 
Not speak for S_D, but there are a lot of different factors ("variables") when designing such a complex game like QFI, especially for the fight sequences...
While I have never programmed a computer game, I have dabbled in programming and can imagine the following scenario for a generic video game:
(A) What is the chance of a fight sequence occurring while you explore the countryside? = range of 0.00 "never" to 1.00 "certainty", which depends upon how stealthy the player is, if they are fatigued or healthy enough to avoid confrontations to begin with, and how prevalent monsters are in that area
(B) What type of monster encounter will it be? = a random number, based on whether or not is it nighttime or daytime and the likelihood of that type of monster being in that particular area (Goblins are 35% of all monsters in the forests, while Griffins are only 3-5% near the mountains)
(C) What are its stats? Single or a group of monsters? What kind of loot/valuables? = a multiple of established base values for that particular monster type, randomly 0.75× to 1.50× for each stat value; a random value for the number of monsters attacking; and a random value for the loot each one would carry
(D) How aggressive is the monster? = a value based on monster type, time of day, and the monster's stats
(E) What are the odds the player can "run away" from the fight? = A percentage based on the player's stats and the monster's stats
and so on...
All of these numbers are added/multiplied together in a formula to result in a single random monster fight occurring.
As S_D said, while it's possible to tweak the numbers with a slider to make the fights easier or more difficult, that might not make the game enjoyable because the resulting gameplay is imbalanced -- and for each "notch" position of the slider, that's a whole other game that needs to be evaluated. One setting = one game; ten settings = ten different games
Coming up with complex formulas that allow the player to make it easier/harder for ALL gaming experiences (not just fights) would be extremely difficult to devise and quite involved.
As I said, I've never programmed a game, so the experts here might say that what I've written here is WAY off base...
