The other reason (besides the inability to chat between moves) was that the board can change substantially in one move (for example, in reversi (or even backgammon)) that it could be even more confusing to new players who maybe just learned the rules. It could (and likely would) also cause many many many complains / comments regarding "My opponent is cheating." or "This game doesn't look right." or "Why did my opponent get to move more than once?" or something like that.