Switch is the culmination of all the past systems. You could argue that it is every past Nintendo home console done right. Not sure if you could say the same of the handhelds though. 

Exactly, all these responses about how its the Wii U done right are correct as well. Basically, the Switch is a celebration of every Nintendo product and platform that came before it. I simply chose the GameCube for this case since the Switch does things better than when the GameCube tried something similar. 

Of all Nintendo's system consoles, Gamecube is perhaps the least like the Switch.

Meh, Gamecube has the weakest first party output of Nintendo's consoles I'd say. Metroid Prime 1 & 2 and Twilight Princess were awesome, and Pikmin 1/2 were solid, but the rest fell short of Nintendo's usual high standards. As a Nintendo fan coming off the N64 I was bitterly let down by the Gamecube's software, and judging by the sales I wasn't the only one.

Odyssey and Breath of the Wild completely annihilate Sunshine and Wind Waker. 

Wind Waker completely annihilates Twilight Princess.

Well the N64 had some great games, but the controller seriously diminish the fun you can have with them. Also N64 games have aged way worse than GC games. Not many 3D games from the 5th gen is very fun to play anymore. Maybe Breath Of The Wild and Odyssey are considered better by most, but I enjoy all 4 a lot.

Nah, TP actually has quality dungeons, a decent art style, and no coma-inducing sailing. :P

GC games have definitely aged better technically, but I still feel like Ocarina is much better than WW and TP, Mario 64 much better than Sunshine, Starfox 64 much better than Adventures/Assault, etc.

I would say Mario 64 is slightly better than Sunshine. Wind Waker is my favorite Zelda game, so yeah. StarFox 64 is probably better, but I enjoy way more GC games than N64 games. Outside of Nintendo and Rare there wasn't much to write home about.

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.)  

True, but Rare + Nintendo both had amazing output in the N64 era, between the two of them we got Ocarina of Time, Mario 64, Starfox 64, F-Zero X, Mario Kart 64, Paper Mario, Banjo Kazooie, Banjo Tooie, Goldeneye 007, Perfect Dark, Conker's Bad Fur Day, Blast Corps, Jet Force Gemini, Diddy Kong Racing...

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.