Being able to handle the ball with either hand comfortably adds so much value to a players game. It allows the player to be able to simply read the defense and then take what is given; rather then worry about only being able to attack with the strong hand.
Most players have a dominant hand that they favor during the course of a game, and even during workouts. That is why two ball dribbling drills are so great. They don't allow the player to be able to switch back over to the strong hand if they get in trouble. The two ball mirror drill is going to force the player to work on both hands at the same time, and then also be able to quickly react to what the other player is doing as well.