I don’t think RPS mini game was a good solution, but the idea itself is worth exploring. I think voting is a neat thing to allow coop players to express their preferences, but I seems very “immersion breaking” to me - something BG3 seems to trying to avoid I imagine with all that fancy presentation.
Conversations happening with the party would benefit both single and coop experiences - considering its DND a dice roll would probably be a more appropriate check rather then RPS mini game.