You do realize that in many games where balance is actually considered in design, the starting player pays for that advantage in some way, like by getting fewer moves on the first turn, a scoring handicap, use multiple games in a match or bonus resources for later players, right? Other games have mechanics such that going first is not an unmitigated advantage. For instance, in Rex, the first player can move to exploit opportunities that open up more cheaply with his move. OTOH, going later than other players means you can counter attack any weakness that opens up, and potentially go for a game winning move without reprisal. Proper design can mitigate the importance of that random roll.
I understand that Reign (which I've neither played nor read) has random generation that assigns stuff randomly instead of determining the amount of stuff randomly, such that random characters are roughly on par with other characters. And our group had more fun rolling up Traveler characters and seeing what happened to them than we did playing the game. The new Gamma World presets your primary and secondary attributes, and then has 3d6 random for the others (with full healing between encounters, and 4e style HP - with 3.x/5e HP and Con rules, Con is so universally powerful that it'd probably have to be set as well) so characters are pretty good at their main things and mostly vary on secondaries.