WARNING: KINDA A RAMBLE, STOP READING HERE IF BORED EASILY.
I've also played a lot of Magic the Gathering, which of course has hidden information and a hybrid fixed start. Both players have the same number of cards in their hand and on the field[1], but will almost certainly have different cards to each other even in Deck X vs Deck X mirror match ups.
In competitive MtG with a best-of-3 system, there can be a sense felt by the players that the die roll for Game-1-Turn-1 has a disproportionate effect on the match. Despite the roll giving you the choice of first or second turns, it is decidedly unusual for players to win the roll and choose to go second (even though the player who goes first skips their first card draw).
For the sake of the argument, if we assume going second definitively has lower chance of victory then the players perceptions can become frustrated and this can effect their desire to replay the game.
Because the loser of Game 1 selects who goes first in Game 2, and will likely pick themselves, and the winner of Game 1 is more likely to have won the Game-1-Turn-1 dice roll.
We get an outcome in which beating your opponent in Game 1 cascades, because your opponent will choose to go first in the 2nd game and either win returning the turn 1 advantage to you for the tiebreaker G3 or lose and the match concludes. Because Game 1 has disproportionate significance AND is the only game where luck decides who goes first AND is chronologically the the first to occur, I have observed (and felt) a kind of stewing frustration at 'playing out' the rest of some matches after losing the die roll and then having a poor early game 1.
I believe a this is mostly concerns players emotions and perceptions about 'inherent' advantages, which is why I've talked about it as a factor of replayability rather than just strategy.
[1]In a typical circumstance, some cards or deck types can alter the initial game state of the board or hand.