For the same reason drums are round and horns are conical.
With light, as with sound, a round cylinder produces continuous symmetrical waves and paths, while a square (or other) shape only produces symmetry about discrete axis’. This is why shapes like pear, oval and marquise have a central, dark "bowtie," and square, rectangular and cut-cornered shapes have dead zones and less overall brightness. The modern round brilliant has the optimal geometry for brightness, dynamic contrast and balanced fire and sparkle across the entire crown of the diamond.
Shape aesthetic counts. If someone has their heart set on a square, oval or other shape it can take priority over high performance. We’d note that most people have never experienced the fire, sparkle and life of high performance diamonds like ours (so consider them please!) but it should ultimately be wearer’s preference.
Diamonds fashioned in the step-cut style, such as emeralds and Asschers, have different optical goals than most other shapes. Step-cuts have long, flat facets designed to produce a distinct contrast pattern and slow, fluid fire in proper lighting. Step-cuts occupy a different space, entirely, than the many modified-brilliants and mixed-cuts designed to mimic the modern round brilliant.