Maybe it's because I never owned a GameCube myself as a kid, but the GameCube controller is the only controller that racks my brain on what buttons are which. I never have to look at a controller even if I switch between PS/XB/Nintendo controllers but the GameCube controller confuses me.
I do agree that the overall shape is comfortable, BUT I hate most of the buttons/sticks. The C stick is gross, I don't care for octagonal stick gates, the dpad is way too small, and the triggers are too squishy and too loud.
Comfort/Uniqueness is the only things I can give the GameCube controller over anything else besides the N64 controller which is a completely irredeemable piece of shit for me lol.
Meanwhile I still use a 64 controller to this day. For a handful of games, it's better to remember the game as it was than to play it with a new controller.
GC is the one I don't get lopsided switching to, because the buttons are so clearly defined. It doesn't matter where other controllers put the "main button", you know where it is here by picking it up and feeling it. The other 3 buttons wrap around A, with different shapes. Once you learn them it's hard to unlearn -they feel physically different under your thumb. It's why Smash players wear it like a glove. In Smash 1v1s with longtime rivals, we generally are open to either GC controller or Pro controller, the only condition is both people use the same one. There isn't really a defined winner, but the playing field has to be 1:1 (VERY important lol). Personally, I never pressed the wrong button my entire Smash career up until using the Pro controller, then it started happening once per 1000 presses or something lol. If you look at a GC pad it's almost physically impossible to strike Y when you really wanted the function on B. The B button is the only button "Left of A" on the GC pad. So every time you want to use a special move it's hard to mess up. But if you have that muscle memory built in, you're liable to strike either B or Y on the Pro. They're both "left of A" and the old B button would fall right between the current B and Y button -and they look/feel the same now.
This might sound silly but little kids and seniors have a much better time learning Kart on a GC pad. "The big green one is gas. The little red one is stop. This is steer". That's it you're done. They won't forget anything, squint at the controller or get upset you want them to understand something complicated. We take such designs for granted. I don't personally need it, but it's made my life easier...
The squishy triggers worked
back then too, especially with the additional button press. Rogue Squadron II is pretty bad to play on anything but the GC controller, because the triggers controlled throttle until the R click, which gave you extra speed at the expense of shutting down weapons. Now when you want to speed up in intense gameplay you need a light finger to ensure you don't turn your lasers off. The game took functions that had been on 4 face buttons, and put them on 2 shoulders. In other words it was less complicated than the last game on 64 (progress) and impossible to recreate now. The shoulder buttons are now useless, because no more games were made to use it since then.
I'm not saying all these differences are critical, just that it worked better than it looked, and it looked that way so it would work.
I must agree the C stick was bad. Going too far differentiating sticks and buttons and carrying over "understanding" from N64. The actual stick head did not need to be a little yellow nub like a C button was, we get it Nintendo. I replaced mine with the normal stick from a wired controller because it was not even good enough for the quick menu in PSO.