EDIT: I've been thinking, if you could somehow make the button trigger a fully pressed resistor value to the resistor line, in other words, trick the GC into thinking the trigger is pressed all the way, THAT might work. Something for Ashen and Zenloc to look into I suppose. I personally will just keep the triggers in my portables.
Game: Metroid Prime 1 and 2
Potentiometer: Used for aiming, scanning, and zooming in/out on the map
Button: by themselves are useless. With the pot, they serve to lock aiming in a specific place or scan an item.
Verdict: Required
Game: Resident Evil (gamecube remake)
Potentiometer: R pot is for aiming, L pot does nothing (aside from zoom function for examining items)
Button: R button is for aiming, L button does nothing, zoom function will be disabled
Verdict: Not Required
Game: Resident Evil 4
Potentiometer: Does the exact same thing as button
Button: Used for aiming, pulling out knife, zooming in/out on map
Verdict: Not Required
Game: Beyond Good And Evil
Potentiometer: R for running, L for crouching
Button: Do not appear to do anything
Verdict: Required
Game: Legend of Zelda: Wind Waker
Potentiometer: L pot for camera control, R pot for crouching
Button: Do not appear to do anything
Verdict: Required
Game: Need For Speed: Underground 2
Potentiometer: Used for acceleration and brakes
Button: Do not appear to do anything
Verdict: Required
Game: Pikmin
Potentiometer: Do not appear to do anything
Button: R button zooms in/out on character, L button re-angles camera
Verdict: Not Required