Button inputs are simply sent to be read by the console more quickly with wires than with wireless signals. It shouldn't be too much of a deficit if you are only at low-mid level play, or don't main a character that depends on frame-perfect tech, but just in case one of those becomes true in the future, it's almost universally suggested to transition to the GameCube controller.
On top of that, GCCs have the advantage of an analog control-stick for more efficient control over movement
(which the Wii-mote lacks), analog shoulder buttons for proper L-canceling
(which the Wii-mote, Wii-chuck, Classic Controller, and Wii U Pro Controller lack; although this issue is limited to PM, since proper L-canceling can be performed with the Z-button in Melee, and doesn't exist in Brawl), simply has more buttons than others and in turn has more button input options
(which is the case for Wii-mote and Wii-chuck; Classic Controller and Wii-U Pro each have 1 more shoulder button), and a second analog control-stick - the C-stick
(which the Wii-chuck lacks) - that's essential for performing several mechanics necessary for competitive-level play. They are: performing retreating aerials, D-airing without fastfalling, B-sticking, efficient button-mashing while simultaneously DI'ing, and DSDI (although this one is only relative if you plan to play Brawl; it's not in Melee, and...iirc...PM).
Regardless of these technical reasons, GCCs have also simply been the Smash Community's controller of choice for years. If you want to play at someone else's house, they'll probably only have less of your controllers of choice than GCCs; even if they do have them, you may have to share if you forgot or couldn't bring your own. If you go to a tournament, it's almost always strictly forbidden across all competitive gaming genres, due to (among several other major reasons) their lack of reliability in terms of batteries dying, signals getting interrupted/dropped, etc.
At the end of the day, you're controller of choice is always...well, your own choice; nobody is gonna impose their preference on you, and if they do, they probably just mean the best for you in the long-run of playing Smash (although obviously that still doesn't make it any less wrong of them for doing so lol). But in terms of the technical and convenience pros/cons of each, the GCC is superior. Dismissing the drawbacks of wireless connections, however, they can be ordered by their efficiency in the following order:
- Wii U Pro & Classic Controllers
- GCC (if not in PM. In PM, it's tied for first, depending on your preferences for (1) more buttons or (2) the option to hold in a Y-Claw position and properly L-cancel)
- Wii-chuck
- Wii-mote