Is it possible we could add the GameCube's GB Player as a platform to submit runs with, or is there a reason as to why it's not an option already?

According to gbrunners.com it doesn't have any advantage compared to a Super Gameboy 2 so I'd say it's fine. It's probably just categorised as SGB2 then, I'm not sure how other games show runs using it.

Hello!

I'm one of those GBRunners :) The GBP is totally valid for runs, but a small note on it:

The standard software for the GBP, the startup disc that came with it at retail, is known for it's blurry output and slight input delay; but it's totally valid to use if you want.

If you wanted to fix that, or just don't have the startup disc, then there is custom software for it known as the Game Boy interface (GBi) that resolves those issues; but requires a bit of work to install.

Good luck on your runs!