The mini-DVD didn't really prevent any game from coming to the system. If you ran out of disk space you could just press a second disk for 10 cents, no big deal. It's not like if they had used full sized disks suddenly they'd have sold double the amount of Gamecubes. Now if the N64 had used any kind of cheap optical disk media, it would have sold way more, the cartridges were far more restrictive, expensive, and far more of a problem that held the N64 back.
The GameCube "failed" because of Microsoft primarily and because it didn't have a trifecta of system sellers that the N64 did.
Microsoft overcrowded the market with the XBox and effectively split the 2nd place standing between GameCube and XBox. Otherwise the GameCube probably could have sold 40+ million units, Nintendo's goal was in that range.
Super Mario 64, Zelda: Ocarina of Time, GoldenEye 007 along with Mario Kart 64 primarily sold the N64, but the top games on the GameCube didn't stack up. Mario Sunshine, Zelda: Wind Waker, Metroid Prime and Mario Kart: Double Dash were no where near as popular, though Super Smash Bros. Melee did take off. That wasn't enough though. They needed basically what was Super Mario Galaxy, Zelda: Twilight Princess, and a more mainstream FPS shooter to match what GoldenEye was for the N64.
MS never should have made their own console, they just overcrowded the market and wasted a bunch of their own money for no good reason. They had some worries about Sony, they could have just staked Nintendo and become a Nintendo exclusive publisher, bringing games like Halo on console only to GameCube (while being free to have it on Windows PC) and gotten more or less the same benefit. In exchange I think Nintendo could have accepted to use whatever Windows OS for their dev kits. That would have worked out better for the both of them.
