Wouldn't it be better to reverse the order of sequential so the last person who signs up goes first? Its not a big deal, but may save an entire day because they can go as soon as they enter the game.
I'd argue that not everyone in a game joined randomly. You have the person that created it and the last person, whom some would say intentionally chose their spots.
Personally I don't mind what the order ends up. No matter who takes the first turn there is inevitbaly going to be a wait.
I think making the last person signed up first would be good. Another idea i had was for team games to mix up the order so it alternates between teams instead of having it go through the people from the top.