It's a mixture of things that suit the game more than any other controller.
The layout itself fits well into Smash because the larger A button right dab in the middle is much easier to press than on a diamond layout controller. Your finger, for the most part, will just be resting there and the speed of the buttons of where it registers your press is very swift on a Gamecube Controller. Another factor is how your thumb can go from B to X almost seamlessly since they are near. You don't have to really move your thumb as much as you would on another controller.
The triggers aren't typical triggers, they press downward and feel like they cup your finger perfectly so, it feels comfortable, and it requires less effort to press them since they go down instead of gun type triggers. Of course, controllers with buttons instead work fine too. However, I feel in the case if you were to compare the Wii U Pro, Game Pad, and the Gamecube's, the softness of the Gamecube's feels more comfortable. The overall shell is also extremely comfortable to hold and accommodates hands of all sizes for the most part.
As for the analog sticks, the octagon gate helps with accuracy for inputs, but outside of that, the stick on the left with it's ridged design feels more accurate to use. I also feel the way the Z button is styled it feels real quick and easy to press and the button isn't too large so you may swiftly grab someone compared to other controllers.
It's honestly such a fantastic controller and is practically perfect for Smash Bros. and Mario Kart. I'm very glad Nintendo gave us the option to use these again.