I don't think it's possible to play decent tennis with only one arm working, the other along for the ride only.
We need balance more than anything else, and the oft arm balances out the hitting arm for the hitting turret of the shoulders.
When we run, we swing both arms. Stands to reason, if we're really hitting the ball hard, against a hard incoming ball, we need both arms working for the good of our balance.
Balance separates the good players from the bad.