How does that generalize to three dimensions?
If you've seen a stack of spheres, with the bottom layer in rows offset by one radius such that each sphere touches six others at the same height, and the next layer nestled in the intersections of this bottom layer, that's a hexagonal close packing.
Also, the "hexagons are the bestagons" attitude generalizes to three dimensions by dismissing face-centered cubic packing as an inferior way to look at the arrangement.
To generalize the Youtube video aspect, see also this Matt Parker/Steve Mould video on spherical packing: https://www.youtube.com/watch?v=3inLMXcetUA
Wouldn't a packing that is irregular in all directions be more robust?
In the "bestagons" video, it is explained that the hexagons win because there are no straight lines in the packing, but I'd expect these to correspond to planes in the 3d case.