After having played several tournaments, I feel the initiative rule is the only one that I really dislike. A mere 1-2 points (or even worse, a dice roll) decide who has the initiative, something that can have an enormous impact in the game.
To me, it's like calling heads or tails to see who will play with a team of 10 instead of 11 players in a football game... Deciding field side (or asteroid placement) on a coin toss feels OK; deciding who'll move first seems poor design. Maybe it was not so important when the Core box came out, but now it is.
Now, why not just use alternative initiative? Basically an initiative token that would switch sides at the end of every turn. Has anyone tried such a thing?