I didn't want to make this until now, because I wanted a video for it before saying/explaining it. So, why is there no Backwards Compatibly for this game on Wii, X360, and, I guess, PS3? I also wanna know if it's allowed, since I did a speedrun on it and I want to know before submitting it.

(I think both the Gamecube and Wii have the same load time, while Xbox is about 2 seconds faster than the X360, but I only tested the beginning, IDK about PS3 though) (Note: I only tested the X360 and Xbox versions, but I think Wii and Gamecube versions are hopefully correct)

Wii, Xbox 360, and PS3 are allowed. You don't see it mentioned on the leaderboards because the games were not released on the newer platforms. A general rule for speedrunning is that if you can play an official copy of a game on official hardware with official means, it's allowed. There are very slight differences between the newer and older consoles for each version of the game, but not enough to justify listing them separately.

I would argue there's a slight advantage to playing say Wii vs GC, or Xbox OG vs Xbox 360 (in this case perf is a bit worse).

Yet it is still categorized the same. That said I would be surprised if any of the GC submissions are actually on GC instead of Wii, so it seems moot anyway.