Being a good ball handler requires the player to able to dribble the basketball while keeping their eyes and also being able to see the floor. Also the player must be able to dribble with either hand, and be able to get where they need to go on the floor with their dribble. If they are not able to do these two things as a ball handler then they are going to struggle, especially as the competition gets more difficult.
The follow the leader alternating 2 ball dribbling drill is going to force the player to dribble with both hands on the move and also keep their eyes up to see the person that they are following. There are a lot of different types of basketball dribbling drills that you can use, but what makes this drill good is that it creates a situation that is more difficult than it would be in an actual game. That way when they get into an actual game they are more than prepared to handle only dribbling one basketball and seeing the floor. Another great type of dribbling drill that add extra difficulty like this is tennis ball basketball dribbling drills.