It's not. Nowhere near powerful enough, CPU wise, especially so undocked. The Shield TV isn't powerful enough for consistent, playable GC emulation, and since the Switch's SoC is an underclocked, lower spec version of the Shield TVs it's simply not going to work well enough for "Nintendo quality" VC. GC VC, if released at all, will require ports (which is more likely seeing how they're having Nvidia develop Wii ports for the Shield TV), or lots of inaccurate hacks, something Nintendo likely wouldn't do.
As to a "GC Classic", as mentioned it's not old enough, and cheap hardware isn't at the point where it could easily emulate the Gamecube yet.