There really isn't room on the market for three traditional consoles to succeed, there never has been.
In order to carve out its share Gamecube would've needed to convince consumers it was a better choice than PS2 and Xbox, and when those systems were delivering on megaton exclusives like Halo, Metal Gear, and Final Fantasy, plus better third party support, DVD support, better marketing, and looking like cool and serious pieces of hardware, there just wasn't any reason to buy a Gamecube unless you absolutely had to play Nintendo's games, and even those were at a relative low in terms of appeal at the time thanks to weird design choices.
In addition to the nostalgia that forms naturally over time, as Jumpin points out, the system has attracted a certain hipster-ish cult appeal in the years since in the way that a lot of failed systems do, when they're seen as cool precisely because they weren't popular.
As such, the internet tends to paint an unrealistically positive view of Gamecube as this amazing system that should have succeeded, when it reality it got pretty much everything wrong, from software to marketing to disc format to the controller to the way it looked.
