Please investigate the functions of the right hemisphere of the brain.
Therein lies the problem with your hypothesis. Speech, language, and hearing, for example, are not centered in just one side of the brain. The Broca and Wernicke's areas are not the only areas of the brain that for these activities. If it were, then some stroke victims and even Gabrielle Giffords (a left brain injury) would never recover their speech and/or hearing. Gabby's TBI went from back left to front left, according to WebMD: http://www.webmd.com/brain/news/20110109/gabrielle-giffords-brain-injury-faq Yet, she speaks and has made an amazing recovery, that I, who has only a BS degree in Psychology, didn't think she'd survive, but I also know TBI victims often do surprise us and make amazing recoveries.
That part of the brain controls vision, language, and the ability to move the right side of the body. All of these functions are at risk, notes Keith L. Black, MD.
It's a very, very serious wound. About 90% of people shot in the head do not survive, David Langer says.
Gabby beat the odds and is still beating the odds, in part because even the adult brain can form new connections and new cells.
Then there is Phineas Gage- a very interesting very early case study of brain injury. There are various places in both sides of the brain for these activities. Not only that, we use most of our brains most of the time, and not just one side, unless, like asanta pointed out, one has a surgery either removing one side of the brain or clipping the corpus callosum and even then, the brain has an amazing way of recovering, esp in children.
So even this hypothesis you've seemed to have stated doesn't hold up to research and actual case studies of TBI and granted, the two case studies of TBI I mentioned are left brain injuries, the same holds for the right side of the brain and neither side exclusively controls a given action.