Sounds interesting. The only thing the U has over the Switch is its retro library. That gamecube rom sounds like sufficient reason to dust off the ole U.Wii U is awesome and I recommend getting one.
They actually are gamecube compatible straight out of the box, however for some reason Nintendo built in a block to keep it from running gc discs. You can put gc roms on an external hd and the wii u will play them natively. But not everyone is comfortable dealing with roms and for me it kind of takes away the retro collecting aspect of finding the games in the wild and playing them on original hardware.
Also there's a huge library of good wii games available on top of the gc and wii u libraries.
You can even get stuff like HD Retrovision wii/wii u component cables and run a wii u on a standard def flatscreen (ie Trinitron) if that floats your boat. It was fun to see Breath of the Wild running on an old tube tv and actually looking pretty good.