Switch emulation works pretty great. But be advised; there are problems with getting Mariokart 8 Delux splitscreen working; the game tends to soft lock on the controller applet. Rayman Legends the complete edition has no such problem and I've had a blast playing with my family.
PlayStation 2 works great and can even be pushed to render games at higher than native resolutions. I'm currently playing Spyro The Eternal Night and Ratchet Gladiator.
Since it can run PlayStation 2 that good I don't see any problems with the Deck running GameCube or Wii games... Except for the instances where Wii games may need motion controls.
PlayStation 3 requires fiddling with the settings on a per-game basis. And then still you'll probably have to downscale the native resolution and limit the framerate on games to make them run well. But the PS3 emu comes with FSR built in and I can't really complain.