Of course, but you also needed a special cable for the GameCube's 480p output and the Xbox's 720p output.
Less data means finding the data faster.
Also "no loading times" is a lie. Cube games HAD loading times. Most of them actually. First party developers were smart enough to either hide these loading times somehow or order the data on the disc in such a way that needed data is accessed more quickly.
Of course, these loading times are in absolutely no comparisons of the clusterfuck of loading time we have on current gen consoles...
This is true, Nintendo and more first party titles were just better at streaming and hiding the loads than most other developers on the system. But their dev kit also enforced the DVD loading times so the developers had a better idea of real-world performance.
Probably their best work in terms of hiding load times and maximizing streaming was Mario Kart DD.