In HCI terms, the Gamecube didn't do much. But it was Nintendo's single largest leap in architecture and hardware power—it sticks out above their console "power curve" trend-line quite strikingly.
The Wii was basically just a higher-clocked (~2x CPU and GPU) Gamecube—much more like the XBO S or the PS4 Pro are for this generation, than like the architectural reinventions Nintendo usually gets up to. The fact that it seemed like a whole new console with new capabilities for games, is more than anything a statement of how much untapped potential there still was in the Gamecube's architecture at the end of its life, that Wii developers went on to find.
The Wii was basically just a higher-clocked (~2x CPU and GPU) Gamecube—much more like the XBO S or the PS4 Pro are for this generation, than like the architectural reinventions Nintendo usually gets up to. The fact that it seemed like a whole new console with new capabilities for games, is more than anything a statement of how much untapped potential there still was in the Gamecube's architecture at the end of its life, that Wii developers went on to find.