Suppose you wanted to rebalance the rules of chess so that the black pieces had equal odds. You really only need to achieve this at the superhuman skill level, and then you could let the matchmaking algorithm could do the rest of the work.
You can construct counterexamples too! For example, "on your turn, say a number. First player to say a number that is double a number the other player said, wins." Is a perfect (I think you mean perfect information) game.