I suspect at least one advantage is having the first chance to play your event cards.
Furthermore the Benefits from Staff is limited based on the number of players minus one. I
2 players = 1 slot
3 players = 2 slots
4 players = 3 slots
In a 4 players game If i play first and I need to 2 more dancers I can give 2 favor tokens to Monica the Stage Manager and I will fulfill my orders. The 2nd player will be able to use once Monica the Stage Manager and the rest players will need to search other tactics to fulfill orders.