I have found that if I learn a unilateral skill with my left hand first, I tend to retain the ability to use that hand. Whereas if I start out with my right hand, I never seem to make the connection with my non-dominant hand. It is pretty easy to go from non-dominant to dominant, but the other way around takes a long-term dedicated effort.
As far as benefits go, I'm not sure. Some imbalances cause problems and others don't. Sometimes correcting an imbalance actually results in a lot of problems. It is highly dependant on the situation. As an example, one high level sprinter leaned slightly to her left as she sprinted. After a few months of chiropractic adjustment and training, they corrected the imbalance, but her sprinting times went down!