and when do you finish the phase? It could get into a deadlock that I do not play my card until you play yours, and vice versa.
Also, it gives an advantage to the Host...normally he has a disadvantage (going first), but that is not the case anymore.
Everybody just plays their cards. No designated person really goes first. People just play cards until we're in agreement that everyone is done. We ask if everyone's ready for market and we proceed. So there's no real locking of the game.