One of the major problems with the Gamecube to be honest was that Nintendo's first party software, one of their core selling points, weren't up to snuff.
After the epic Ocarina of Time, Mario 64, and Starfox 64 for instance, a Zelda game that looked like a children's cartoon, Mario being a janitor, and crappy on-foot Starfox weren't what gamers wanted.
Compared to the N64 before and the Wii after, the Gamecube badly lacked killer apps.
It was just a fucked up situation.
With the N64, Nintendo and Rare were on fire software wise, but poor hardware decisions and Nintendo not listening to 3rd parties killed them.
With GameCube, they took great care to make a good piece of hardware with cheap optical disc media and mended fences even with Namco, Capcom, Konami, kinda with Squaresoft, etc. but Nintendo's 1st party efforts were underwhelming and Rare was gone outright.
If you could give Nintendo what the GameCube was but scale down the power for whatever would have been realistic for 1996 in place of the N64 hardware ... Sony is never the market leader IMO.
And/or paradoxically GameCube badly needed Mario 64, Zelda: OoT, GoldenEye equivalents and didn't get them. Even Mario Kart: Double Dash was no where near as popular as Super Mario Kart (SNES) or Mario Kart 64 (N64).