Playing your turn at the same time as another player leads to issues, like not seeing what they are doing until you do something, and being able to take instant win victory conditions and then when the turn rolls over, wait for one player to start their turn and then starting your turn during their deployment, autowinning the game before they had a chance to affect the game state.
Basically, I love freestyle play (greatly speeds up the game and adds a little unpredictability) but I dont think players should be allowed to take turns at the same time. Once a player starts a turn, make the acting player finish his turn before the next player can start.