GameCube did have good third party support it had pretty much all the popular Western third party stuff minus GTA. From Japan they had Resident Evil exclusivity, Viewtiful Joe exclusive for a year, Metal Gear Solid: Twin Snakes, Tales of Symphonia, Phantasy Star Online exclusive, Sonic, etc.
GameCube released a year too late, with a off-putting toy-like design, and they made mistakes with Zelda and Mario and not making a proper successor to GoldenEye/Perfect Dark. Also losing Rare and getting no one to replace them was problematic.
So they made a lot of errors with the GameCube which cost them.
SNES, NES, and GameCube all had good third party support.
N64, Wii, and Wii U did not, but there are clear reasons for that ... the N64 because of cartridges, Wii and Wii U because they're a full generation underpowered versus their competition.
