I honestly don't think there is any advantage/disadvantage to going first in Innovation like there is in some other games (I'm looking at you, Dominion). At least not in 2p anyway. There is a reason why the first player only gets 1 action, and it's a good one. After any player's turn (any turn) they have had exactly one more action than their opponent. Then their opponent plays a turn and has had exactly one more action than them. It's pretty well balanced this way, and I'm pretty sure it negates any potential first player (dis)advantage.
Edit: The alphabet thing is just a slightly different way of choosing the first player. I'm sure you could roll dice for it, or R/P/S for it, or winner/loser of the last game for it or whatever, and it wouldn't change the outcome of the game at all. I, personally, like the alphabet thing. It's different and fun. I think Carl Chudyk likes the alphabet thing too, as I've recently read the rules to another of his games,
Glory To Rom... Uchronia (due to it being the BGG comp), and that uses exactly the same method of choosing a starting player.