For online players, a chat window in the exchange window is not needed at all. It's a waste of game time. Communication usually happens at the start, and also when a player is waiting for their turn or is in battle.
However, the aspects related to saving game time are interesting.
Could it be possible for the turn timer to start after a turn is taken (and 'Ok' is pressed in the notification window), rather than as it is now - where time runs independently? Also, there are times when, in the last second, you gain experience from a Pandora's Box or another event, but there is no time left to choose a skill when leveling up; everything is done automatically.
Could it be possible to set the turn time in the settings - 3 minutes, 5 minutes?