Not having games like GTA3 hurt, but Nintendo hardly ever gets the same level of multiplatform support as their competition. Nintendo themselves should be seen as the main variable that went wrong.
The GameCube was basically the N64-2 as far as Nintendo's software support went. Most of the best-selling GameCube games (Super Mario Sunshine, Double Dash, Wind Waker, Melee, Mario Party, etc) were basically less-revolutionary successors of N64 titles. And the N64 wasn't that popular to begin with, so getting a few more multiplatform games was not that big of a deal, especially with Rare out of the equation after 2002 (4 of the top 10 sellers on N64 were Rare games).
It also didn't help that Nintendo seemed to give up on the GameCube halfway into its life. Look at the N64; it didn't do amazingly, but many of it's biggest games were released in its fourth year or later (Super Smash Bros, DK64, Majora's Mask, Mario Party, all the Pokemon games, etc). How many big GameCube games were released from 2004 onwards? You had Pokemon Colosseum, more Mario Party, and Mario Strikers basically.
Love and tolerate.
