Is that because the innovations are so powerful and impactful that they massively change the game state? I wonder what the designers could do to make the game more playable in a group.

It makes me think of one of my group’s favorite games, Cosmic Encounter which sees you leading an alien race with a game bending special ability. Each round is a quick duel with a random player so you can’t plan too much around that. The strategizing is mostly around when you decide to use the best cards in your hand, which you don’t typicallyhave to worry too much about being taken from you. Also you often have to decide which player to hinder from winning or to help (perhaps opportunistically, even if you don’t want them to get stronger it can pay to hitch your wagon to them for a boost).

We just like the surprising moments that can arise from the alien abilities and the cards. And the full-table engagement with most rounds.