I don't know where the flaw is in your reasoning, but what I will say is that the proof is in the eating. IGN head-to-head comparisons make for pretty consistant reading - with the XBOX version looking best and running the most smoothly, followed by the GC and then the PS2.
Personally that doesn't bother me - I brought a GC because I like Nintendo's own titles (Mario Sunshine, Smash Bros, Zelda TWW, Mario Kart DD, Metroid Prime) which are not available on other platforms.