I subscribe to the emergent properties theory, that our consciousness is an emergent property, same with our intelligence and the two different personality traits that appear on the brain being split into two hemispheres are on that path.

I do wonder though if being split introduces any differences from being born with a split, as in does being part of a whole create those traits or if those would've happened regardless of when the split happened and being whole works like you described with some personality traits suppressing the others.