Credit to Sony too ... they were fucking taking no prisoners that generation.
They got up to a 20+ million headstart and would not let off the gas, locking up FFX, MGS2, and GTA3 exclusive. Even if Nintendo did a lot of things right, they would have been in tough, and MS was not the Panasonic 3DO type push over either, Halo being such a big hit gave them instant credibility within the game market.
The competition was simply very strong. Even if they had whatever game you think they were missing ... great 2D Mario, great 3D Mario, great Zelda ... they probably would've still gotten beaten badly by the PS2.
It was a different time too, the NES generation was getting into their late teens/early 20s and wanted a console that showed gaming wasn't a kids past time. PS2 fit that image much better than GameCube. Now that the industry has aged more, that mentality isn't as destructive to Nintendo. Gaming is more established as a mainstream thing, you don't need to explain yourself if you're an adult who plays games but that was still a thing in the late 90s/early 2000s.
Adults didn't want a console that looked like this in 2001:
With this as a killer app:
