In order to present it as a mental illness there would have to be some kind of negative effect, wouldn't there? These differences you mention don't stand out as harmful or even disadvantageous.
southpaws are more common where at least one parent has schizophrenia. i believe it to be caused by an epigenetic change, where damage to the brain in a parent leads to the parent rewiring their brain to use the opposite hemisphere.
In short, it's hardly an illness, more of an antibody to one.