Of course! The Wavebird is my go-to controller in Mario Kart and Smash Bros, though I feel little negativity towards the wii-mote unlike a lot of people. I thought it worked great in Galaxy and Twilight Princess. As for your point on Nintendo not doing better, start from 2002, the Wavebird was a huge improvement over being tethered to your gamecube with only 6 feet of cord.
Once you get used to playing Melee, using a Wii Remote in Brawl is a step back. Besides, Masahiro Sakurai even said Brawl was made for Gamecube controllers.
All the other good games control amazingly with Wii Remote though.
This it true 2002 and my Wavebird is where its at. But from that point...
The original Gamecube controller was always way too small for my hands. The buttons were also too small and my thumb could mash all the face buttons at once. They are pretty worthless when it comes to games requiring two full-size thumbsticks. I always liked the tactile feel and responsiveness of the Gamecube's thumbstick over the others. For the majority of games though, give me a DualShock or a 360 controller any day. The thought of playing Halo 3 or inFAMOUS on that little thing is cringe-inducing........
The funny thing is that the Gamecube sold horribly compared to competitors because it wasn't innovative in anyway (btw, Nintendo basically invented Rumble, Analog sticks, face buttons, the D-Pad etc).