Having the rule does a couple things.
1 - When there is any question or hesitation, a dealer can correctly state that every hand must be exposed. It's much simpler than saying, OK, you two first, etc., and avoids the accidental muck problem.
2 - Even when everyone is prompted to show, there are slight delays. During that delay, a side-pot player might see an all-in player's better hand and fold their hand, even though they might have won the side pot. Because of the rule, the dealer can correctly try to prevent the folded cards from mixing with the muck pile and becoming unidentifiable.
3 - If mucked cards do become unidentifiable, and the player then complains about it, the floor person can say "That's why you should follow the dealer's instructions / know the rules."