Yeah but it's like if instead of the DS having 4 face buttons it had only 1 with the assumption being that the touchscreen would make up for the lost button. The DS controls just built onto the GBA's. Nothing was removed, only added. You can't just play a Gamecube game on the Wii controller. The idea is that the remote's unique features are supposed to replace the functionality that came before it.
Actually, C-stick aside, the Wii controller is only one button less than GC. In that respect wiimote is only slightly less functional, and this missing functionality is made up by the pointer/accelerometer/gyroscope inputs. Sure, you could add another button but that isn't going to solve the 3rd party situation. And you can play GC games with a Wii controller. Prime Trilogy demonstrates this, as does Mario Galaxy. I'm actually curious now, can you name a GC game that wouldn't be possible on Wii, even with small adaptations (other than fighters; I've heard you use this one a million times)?
The Wii forces you to try something different while the DS gives you the OPTION to to try something different. The proof is in the pudding. Both systems are the clear market leaders yet the DS has very good third party support and the Wii has arguably worse third party support than even the Gamecube. The Wii is the ONLY market leading console to have the worst third party support of it's generation. That suggests to me that Nintendo did something wrong that they did correctly with the DS and this seems like the likely scenario.
I would not blame the 3rd party situation on the controller. It might have been a factor in select instances, but almost all games are playable using the Wii setup, as evidenced by the wide representation of various genres. In fact, I remember hearing a whole lot of developers get excited when the controller was originally revealed.
The main culprit behind the poor support was the perception that "only casual gamers play Wii, and they only buy crappy party games". And it's still a misconception, explaining why Reggie has to interrupt his 'presentation of a lifetime' to remind us that Wii is still outselling the other consoles combined, and that Wii gets played more by its owners.