I didn't know that until this post lol. And it was released when I was 12 and actually into gaming. Now I find it weird that the "controller" is so weak that it can't do anything but stream from the console, it kind of make the portability useless.
Main thing I used mine for was continuing to play a game when someone else wanted the TV; I could just switch to "display on controller" and keep going. Not such a big deal these days but back then it was pretty nice!
Asynchronous game design is something that holds a lot of promise. Traditionally, that was something reserved for online multiplayer in PC games. But suddenly it was possible to design local coop around one player interacting with the game in a different way than the others. The idea is still really cool, but I think most devs are unwilling to experiment with such a niche product.
Zelda four swords adventures managed that on the cube already. Not quite suddenly, I'd say. Awesome game if you had 3 friends and the necessary hardware.
The idea was to have two different screens displaying different information and there would be interactions between the two. Like the Nintendo DS's two screens. I played a tech demo(?) at the store where you'd aim a bow and arrow with the Gamepad at a target that was on the TV.
The idea didn't really end up panning out for most games.
Critically, it could stream something different than what the console was rendering to the TV. At the time it seemed Nintendo was hoping for the kind of design explosion the DS had early in its life, and a few titles trying such things were really good, but for many reasons it didn't stick the way the DS did.
Especially considering a lot of Wii buyers were not exactly deep gamers, but very casual customers.