and thought about all of those circular craters, then realized that the circularity of the craters is a consequence of symmetry (and also of conservation of energy). The sphericity of Mars itself is also a consequence of physical principles like that.
So in terms of physical laws and physical phenomena, n-balls show up much more readily than n-cubes, and in some senses have a much simpler description.
If you weren't already on a street grid in a city and using that grid to navigate, a parent might say to a child "don't wander more than one kilometer from home" and would naturally generate a circle rather than a square as the locus of points that are close enough.
Nature and people care a lot about proximity, which is to say distance, which then generates n-balls. So maybe they are more fundamental and more intuitive for certain purposes. But the curse of dimensionality is going to make either balls or cubes weird in enough dimensions, and counterintuitive to intuitions formed with just three dimensions. The balls are going to be surprisingly tiny ("there's very little nearby here") and the cubes are going to be surprisingly vast ("space is so spacious").
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