Because all the maps are symmetrical, if the person going first on a small map simply skips their first turn, they’re now in the same position as the person who went second, only with a TWO key advantage instead of one. In other words, going first is worth 1 key to the person going second, but 2 keys to the person going first.
Just a thought. 
Not quite, the overall keys you get for a whole game also matters here, player 2 has an extra key to the overall amount of a game, and this is because player 1 can have early board presense. You may skip a turn and have some extra keys, but at the cost of board presense (keys on board) and position advantage. You also need to kill 1 extra key to finish off all of player 2’s phobies.
Exemple: If you bring out a 6-key unit one turn late, I maybe already have 2, 2-key units, and pull out a 3-key unit. I will have 7 keys on board, and better positioning to prepare an assault.