I've probably remembered something wrong here, nevertheless the centres of all adjacent hexagons are of equal distance to the centre of the central hexagon. In contrast, a square sharing one vertex (diagonally adjacent) with the central square is farther than the square sharing one edge.

That's only if you use a scaling factor of 9 instead of 4.

edit: Wikipedia tells me hexagonal tiling is conjectured to be the tiling with the smallest perimeter per cell, and is the densest way to arrange circles on a plane. So that's a big plus when binning.

Click through gets you at http://mathworld.wolfram.com/HoneycombConjecture.html, which shows it is not a conjecture anymore. It was proven in 1999-2001 (I do not know whether the ArXiv version needed improvements)