I've never played a Smash Bros without a Gamecube controller, because I'd rather not use the Wiimote when I've played it on the Wii, but I don't think there'd be any issue using the Wii or Wii U Pro Controller over the N64 controller as long as it works.
If the Pro Controller works, there's nothing that the Gamecube controller can do that the Pro Controller can't. One reason why some people make the comment that it's the best Smash controller and reading through two pages I haven't seen one person mention it, the C stick. Yes, you can do smash attacks with up, left, down, and right plus attack, but the C stick is more efficient, as not only will you never fail to do your smash attack, you'll be able to do the smash attacks quicker, even if slightly. As long as one of the Pro Controllers allow the right analog to replace the C stick, then there's really no need for the GC controller.
I always call people sheep a lot, but it's opinion I have that most people just follow the popular opinion and I think most people who say the GC controller is required to play SSB are just sheep following the popular opinion.