Iwata became president in 2002, not 2004, and before that he was the head of "Planning" and was supposedly a key figure in the design of the GameCube.
NOA was largely responsible for hooking up with Silicon Graphics and the N64 (not the decision to use carts). That relationship gave birth to the ArtX graphics card in the GameCube, which was the only real strength of the GameCube, and pretty much carried the system. NOA also hooked up with a lot of the Western developers who made the N64 worth owning. The N64 was all about Mario and Zelda, but it was also the Halo box (back when such a thing was called Goldeneye) and had a lock on the developers who would go on to make Grand Theft Auto.
NCL decided that NOA needed to be "managed", so they made Iwata the head of "Planning" in 2000, and he took over third party relations (and subsequently killed them) and made sure that the GameCube reflected Nintendo's flawed ideals. Yamauchi, not Iwata, was directly responsible for the selling of Rare, but NOA were the ones who brought Rare into the fold. Yamauchi might have kept them around if he had been listening to NOA instead of Iwata.
The DS, as a strategy to counter to the PSP, supposedly came from Yamauchi himself, as did the idea of dual screens.
Waggle was in the pipeline as a late-life GameCube add-on, and AFAIK it was Iwata's decision to keep it in reserve and use it for a GameCube relaunch (which was his idea, and became the Wii). Waggle's origins don't lie with Iwata, but it's successful implementation does.
