Single Comment

Being a non-mathematician, and being obsessed with 'fairness' in my game
designs, I see symmetry in a starting setup as one way to quickly indicate
the 'fairness level' of a game. It says visually that everyone starts out
equal. On the limited boards we generally deal with in chess variants, this
equality is important to play balance, and thus speaks to the interest and
fun of a game. It is not something that is required. But asymmetric games
are generally wargames, incorporating larger boards, terrain, varying
placement, movement, and victory rules and multiple modes of capture. To
stray too far from symmetry in variants is to risk designing oneself right
off the fringe.

On the question of what the effects of bilateral vs radial symmetry, I'd
suggest switching the necessary pieces around and playing the 'same'
game both ways to see what happens. In my limited experience with this, I
found that tactics and strategy can change, with a symmetrical attack by
black able to be developed in radially-symmetric games, where the same
tactic of mirroring the opponent's moves can lead to quick defeat in
bilaterally-symmetric games.