I really think the Gamecubes major failing was the marketing.

If the console headline color wasn't purple and their commercials weren't seemingly all aimed at children they may have attracted sufficient market share for third party developers to invest more in the console. It was a neat little box but unless you adore nintnedo first party offerings it again was another Nintendo-Fans-Only offering by the company. It had a few good third party offerings like the Resident Evil 1 remake and Zero but I honestly can't think of any great exclusive games outside of the Zelda, Metroid, Mario team.