Your logic is so tautological. They're successful because they're succssful. Well, yes, but if Nightfire was Halo, wouldn't the Gamecube have won the generation since it had Nightfire on it?
Who cares about "winning the generation"? That's console warrior nonsense. The Xbox had Halo, yes, and many other superb, fantastic games (Far Cry: Instincts was great), plus the best versions of multiplatform titles, and it sold worse than the N64. Heck, the PS3 and 360 had all those fantastic games, but they got crushed by the Wii. We could argue that the reason the Xbox 360 and PS3 sucked so hard was because they didn't have killer apps like Wii Sports Resort.
I feel like you're approaching this topic from a completely different angle to me. My position is that PD being on the GC would have benefited both the GC, since it lacked "muh exclusive" FPS games, and PD, because it would have benefited from better performance, visuals, and a fresh audience. Same reason why Turok 3 sold poorly and Turok: Evolution sold pretty well. In 2000, the N64 was winding down. Kinda like how the Xbox was winding down by 2005 and Splinter Cell: Chaos Theory sold a fraction of what the first Splinter Cell sold.
Why would they sell systems when the market clearly shows that nobody wants these games en masse anymore?
This is actually kind of a good point, and it ties into the current debate about how much "exclusives" matter in the console space. For example, the market has clearly demonstrated that they're really not interested in games like Persona 5. But that doesn't mean Persona 5 isn't a factor in selling consoles.
I can't tell if you were a GC only player back in the day, or if you're just nostalgic for the days when FPS weren't all Halo/COD 4 clones (I am too! Build a PC!).
I didn't own a Gamecube, actually.