I can't stress how important it is to be able to handle a basketball with your off-hand to have success in the game of basketball. For a right-handed player, putting the ball in your left hand could be the difference between a successful drive or shot, and a steal or block by the other team. Unfortunately, a lot of high school coaches don't require their athletes to use their off-hand when doing lay-ups or ball-handling, and many athletes are too embarrassed to demonstrate their lack of ability in front of others, which means there's never any development. This is where your own practice time is essential. In only 15 minutes a day, you can develop your off-hand and make yourself a much more effective player. When I was developing myself, I would make myself do 50 lay-ups on the left side (which takes about 8 minutes), and then I would put the ball in my left hand and let it go for another 7-8 minutes, doing stationary and full-court drills with the ball ONLY in my left hand. For the first couple of weeks, it was an ugly sight. But, by the third week, my coordination and control had gotten so much better. After a couple months of following this routine, I felt comfortable to keep the ball in my off-hand, and in practice, was a much more difficult opponent to deal with!
I remember watching Kevin Johnson play when he was the point for the Phoenix Suns many years ago. How sad that a "professional" player could not finish a drive on the left side of the basket with the left hand (thus protecting the ball from the defense with the right).
College coaches apparently let this slide as well. A real disservice to both the game and the student.