According to the current rule set, the player who initializes the clash draws the top card from the store deck to add to their played card, then the other players do the same. The previous rules had the players each cut the store deck at random to reveal the card they would add to their total.
Will you be playing with the current rule set as it favors the person initializing the clash or house rule it to have players cut the store deck?
Although it's not a certainty, the likelihood of a base set card to have a lower star value than an expansion set is high so it does add strategy to when a player would want to initiate a clash.
I feel it adds a level of strategy and the top card of the store deck is fine. really with a store deck that big I want to mess with it as little as possible.
also remember with clashing sometimes you want a low value.