Chess doesn't have balance – it clearly favors white due to the first move.
In mapmaking, color has a similar effect.
Asymmetry of moves sometimes matters, sometimes it doesn't, but more often it doesn't, as experienced players try to cover all directions and launch the papa strategically. Situations where a player randomly rushes somewhere and gets a great advantage, which they immediately turn into a victory, are quite rare, especially on h3dm1.