I'm still puzzled why they went with 6 quad-trees, instead of doing an equal-area projection with 2:1 ratio and quad-treeing that instead. You lose a bit for half the map but you do with 6 sides too (takes 3 bits).
Somewhere there's an older doc/presentation that goes into the reasons for the cube in more detail, and if I remember where it is, I'll post it here later.
Consistent uniform cell size, minimizing distortions and relegating them to remote parts of the ocean, grouping land masses together (one cube side is almost pure ocean), optimizing for geodesics, and making it easy to index and reason about were some of the considerations in the design decision. It's been a while so I'm little fuzzy on all the reasoning, but I'm sure someone else on here can provide ptrs or fill in the details.
Edit: it may also be easier to figure out which squares are adjacent when using a grid based on a cube.