I think it´s not a good idea. I can not imagine a game of chess with the white as black and viceversa. In this case, would the colour of the squares change too? If it doesn´t change then the queen black would be on a white square and the white queen on a black square with the current colour squares and in the other case then the right square of the corner it´d be a black square.

I think if it´s not possible a specific solution for each kind of game then it´s better the white starts always the game than playing with the colours changed.