GameCube controllers work on Wii — but ONLY for GameCube games.
Wii games are designed around Wii Remote's unique features (motion, IR, speaker). GC controller is traditional buttons/sticks — incompatible with core Wii gameplay.
Use GC controller for GC games (and those 5 Wii games). For everything else: Wii Remote + Nunchuk / Classic Controller / Wii U Pro Controller.