The regular setup of chess is mirror-symmetric: If you mirror the positions of all figures on the equator of the board (between the fourth and fifth rank) and swap the colours, nothing changes. It is also almost point-symmetric or rotational-symmetric: If you reflect the positions on the centre of the board (or equivalently rotate the board by 180°) and swap the colours, only kings and queens will swap their positions.
By contrast, in Chess 960 a.k.a. Fisher random chess, opening positions are mirror-symmetric by construction, but in general far from point-symmetric. Now, suppose I want to introduce a Chess 096, where white’s setup is determined like in Chess 960, but black’s setup point-mirrors white’s. Castling rules would be point-symmetric as well. A possible starting position would be this:
rnnkbqrb/pppppppp/8/8/8/8/PPPPPPPP/BRQBKNNR w KQkq - 0 1
Like in regular Chess or Chess 960, the only imbalance is that white has the first move – unlike for example, if white and black’s starting positions were randomised independently. My question is: Are there any inherent gameplay problems with these point-symmetric starting conditions? For example, does this tilt the balance of the game?