The recent Nintendo leaks have given us prototypes and source code, but the most recent dump of info is perhaps even more interesting as it pertains to hardware concepts Nintendo was working on during the GameCube era.
According to the leaked documents, Nintendo planned to create a portable GameCube which included a screen and a docking cradle. The machine would be playable using its built-in display, but could also be placed in the dock and connected to a TV. This could go some way to explaining the system's diminutive size when compared to the PS2 and Xbox, as well as the existence of that iconic carry handle.
Here's the specification:
Could such a system have really worked? Given the limitations of modern batteries – let alone those from the turn of the millennium – we'd be tempted to say no, but it might have been interesting to have a system which could be taken around with you, rather like the Sony PSOne with its officially-made portable screen. Indeed, the GameCube itself got a similar product, albeit one made by third-parties rather than Nintendo itself. A hybrid system which boasted such a display as standard and could be easily carried around would have been interesting, if not game-changing in the same way the Switch has been.
Elsewhere in the leaked data there's a potential GameCube successor codenamed "Tako":
This system is perhaps what Nintendo had in mind as a follow-up to the GameCube before it decided to drop out of the technological arms race and instead focus on making motion control the unique selling point for what would eventually become the Wii, which was powered by roughly the same tech as the GameCube.