Nope. Not unless you care about very specific genres. If you were into kart racers, party fighters or just generally Nintendo's output specifically, it was a great console.
If you wanted the best variety, you got a PS2. JRPGs, simulation racers, arcade racers, 3D platformers (outside of Nintendo's stuff and Super Mario Sunshine was a bit of a lame duck for the day), survival horror, rhythm, third-person action, 3D fighters, 2D fighters...PS2 had Gamecube beat handily in these areas for quantity and in most cases also in terms of quality.
If your statement was so true, Gamecube would have seen better sales that gen. Instead even the Xbox outsold it.
This is objectively false. Like, you can prefer select games on it over PS2's all you want.
But factually speaking, its library is weaker both in terms of variety and especially in terms of total games. Quality is subjective but basically if you didn't care for Mario, Zelda, Metroid or Smash Bros there was virtually nothing on the Gamecube the PS2 didn't have an answer for, and a LOT on the PS2 of high quality that had no alternatives on Gamecube whatsoever.