I think I understand your underlying point, and I think I agree. Basically, Gamecube is when Nintendo decided to differentiate their system from the other guys'. They differentiated by doing weird stuff, which mostly failed to add to the gaming experience. They definitely did try to make the Gamecube seem portable, but it really wasn't significantly easier to take with you than PS2 or XB. Switch is actually a portable home console, or at least close to one. With GC, they tried to create controller options (you could hold the controller in multiple ways), but they ended up with a weird, unbalanced thing. Switch has multiple control options that are actually good. They tried to make their existing IPs feel fresh and new on GC, but they mostly missed the mark. They've seem to have done a better job of this on Switch (though its too early to say for sure.)
That's exactly my point. The Switch gets a lot of things right, and like NIntendo and everyone here says, it takes its inspiration from every piece of Nintendo history. But many of its design and aesthetic elements all owe a lot to when the GameCube tried to do them, but failed in doing so.