The gcn didn't exactly have direct backwards to GBA, but it did have that extra little accessory you could put at the bottom for GBA if that counts
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Lml, if it wasn't for 3ds backward compatibility to dsi, dsi downgrades wouldn't be possible tho
Still though, the claim that "every console from Nintendo was backwards compatible" doesn't hold up at all.
Up until the Gamecube, no other Nintendo console at the time had it.
NES, SNES (SGB counts?), Virtual Boy and N64, they all didn't have backwards compatibility, and if they did, was limited as hell (SGB only played GB, not GBC, and the transfer pack only allowed for Pokemon games to be played on the Stadium games).
The ONLY instances of Nintendo holding its backward compatibility was its handheld consoles. All of them have been backwards compatible in some form.
To end it, eShop+External memory (SDXC I hope) is the way to go for the Switch.
I just hope hackers target it to give it the ultimate backwards compatibility as it seems to be much more compatible with multiple emulators thanks to its ARM based architecture instead of PPC, which plagued previous consoles from them.