Let me see if I've got this right.
So in summary, the GameCube's network adapter functionality works so well for multiplayer because was designed for that reason. This may be supported by the fact that it has a custom chipset and the fact that it is accessed via Serial Port 1 and not USB. What's more, the (expensive!) adapter has a custom chipset that, to my knowledge, has never been cloned.
The Wii, on the other hand, does not have Serial Port 1, and I have no idea if some way exists to expose it. Instead, Internet access is the primary focus of the console's network capabilities, so the Wii's IOSes that handle network functionality are not designed for high-speed, low-latency communication. They are what allow games to communicate via Wi-Fi or Ethernet without having to write specific code for each, so they are more of a high-level implementation.
I assume that Nintendont uses IOS to handle BBA emulation, so IOS is the real bottleneck here if I am correct so far. Therefore, the only way to improve BBA emulation would be to use some kind of custom IOS (or driver?) to access the ethernet adapter or Wi-Fi adapter. Of course, Nintendont is basically complete and the BBA emulation is good enough for most people, so I wouldn't expect that to happen.
Please correct me if I am wrong.