I'm participating in my first Battle Royale games and learning how the sequential turn version will take months and/or years to complete. I'm not planning to join any more for this reason. The experience would be much improved if it was faster.
Since the game seems to have a special status (being continuously filled and having a dedicated link on the Game Menu board), I think it would be appropriate to receive some sort of turn prioritization. Participants could be "forced" to take their Battle Royale turn before being allowed to make a move in any of their other active games. I wouldn't suggest applying this retroactively, but for any new Battle Royale sequential turn games it could be part of what you agree to when you sign up.
No need for such a condition on the freestyle turn version.