That isn't true at all.
The GC was supported from third parties in the beginning with a significant amount of multiplatform titles (Dead to Rights, Call of Duty, BMX series, Mortal Kombat Deadly Alliance, Soul Calibur II, and Star Wars franchise quickly pop into mind). It just started losing ground because of its horrid sales (I think Soul Calibur II was the only one that did well of those I listed). The late/crappy versions started happening around 2003.
It's nothing like the Wii's situation at all which seems to be going through the exact opposite. It started out receiving crappy/late ports that did respectably well (Resident Evil 4, Okami, Tomb Raider, Rock Band) to on its way receiving a significant amount of well done multiplatform titles (Shaun White, Call of Duty: Word at War, Guitar Hero: World Tour, Rock Band 2, Tomb Raider, Sonic Unleashed, .etc.) to a progressing future in the multiplatform (Indiana Jones: Staff of Moses, Tom Clancy's H.A.W.X., EA Tennis, EA's Keynote with presenting Dead Space Wii) and exclusive titles (Dragon Quest X, Tales of Battalia, We Ski, etc.)
It does sounds familiar though. Reminds me a lot of the PSP actually.