Within it's own product history Nintendo has done OK, but lets be honest, GC to Wii and WiiU to Switch were almost lateral moves. Sure, the newer consoles are better, but it isn't a "normal" generational gap. The difference between Xbox One and One X is larger than WiiU to Switch, I think. And WiiU released not long before PS4 and Xbox One and struggled to match 360 in many games.
It doesn't really matter why something came out later, only that it did. You would expect a system that came out later to unilaterally outperform one that is older, but with PS3, that was not the case, as most 360 games looked or ran better, often with quicker load times. And Wii, yeah, that didn't hold up next to 360 at all either.
I mean, has anyone here looked at the games that were on Xbox (original) and Wii? The Wii port of FarCry is terrible. The Xbox original is playable. Or how about Splinter Cell Double Agent? The Wii version looks a generation behind even though it's technically a generation ahead.
Here's the thing. Through Wii, we get a good look at what Gamecube could do with a bunch of extra memory, with real development effort optimizing for the system. It even has extra frequency to make it even faster. But I don't think anyone would think it could run Doom 3 and have it look as good as the base Xbox version, much less one with extra memory.