I had a GameCube back in the day no one ever moved it around with the handle. Sure you could move the console but you still had all of the wires and of course the controller to move as well so the handle, and of course you would need TV at the destination so wasn't really helpful.
I never understood who they handle was aimed at.
In theory you could take it over to your friends house but realistically all you did was just set it up where you wanted it and then never move it.