Probably many asymmetrical combinations are unfair to black. Maybe running through combinations and simulated games with a chess engine could identify ones that are fair, asymmetric and fun? Then a database could be built up of these combinations and it could be randomly selected to start your game.

From my understanding that is exactly what this group are doing: https://chess960v2.com/en

Maybe there are asymmetrical combinations that actually give Black the advantage? Because Black's setup is nicely harmonious and White's is clumsy. Or maybe not I'm entirely unsure.

Similar idea is randomized openings. Checkers does this already. TCEC does chess AI tournaments using sharp preselected openings (matchups playing 2 games, one of each color)