There are some situation where your opponent's next move is forced or, if not forced, obvious. How about a provisional move feature where I would make my move and also submit my following move assuming my opponent makes his expected move. Then RHP would make my first move and, if my opponent does as expected, make my following move automatically. Then it would be his move again.
Why have this feature? Speed up games. No need to wait 24 hours or more for one's opponent to reciprocate a Queen swap or get out of check with the one, legal move.