I see no advantage, aesthetic or scientific, in using a different shape for the elements. Squares are ideal because of the two orthogonal relationships of an element - group and period. The periodic table may be regarded as a square lattice on which each element occupies a lattice point. Square boxes are then space-filling, which is useful if you want to include information about the element, e.g. atomic weight, electron configuration etc. Circles, diamonds etc. would leave a lot of white space. And there might be a temptation to try and close-pack them, which would obscure the group-period relationships that the PT displays so well.