Why is there symmetry in animals?
Intuitively, symmetry is useful for balance. A weight-nonsymmetric animal would have to expend additional energy to keep itself balanced (and this would also increase neural complexity for maintaining balance).

Mirror-image pieces only have to be coded once in the genome as a rule-of-thumb, allowing reuse of (mostly) the same genetic pieces with a few orientation and growth-origin markers thrown in. If you put vastly different parts on each side, you have to encode them (making the genome larger with more opportunity for mistakes and harmful mutation)