I asked people who are in the medical field and they say they don’t know and have never heard why, so I will throw the question out to the masses- Why does one side of the brain control the other side of the body, what purpose does it serve and what would happen if say the right side of the brain controlled the right side of the body and the left the same?
As a former Ph.D student in behavioral neuroscience, I will echo the answer that nobody and I mean nobody knows. Neuroscience questions can be frustrating to laypeople because it is among the least developed of all the sciences.
Why are you assuming there must be a “purpose”? Our ancestors who evolved that way didn’t die off before reproducing, that’s why.
All vertebrates have this crossover structure, which would indicate that this structure developed very early in our evolution. Some invertebrates have crossover structures as well, which some folks think is more evidence to suggest that it provides some sort of evolutionary benefit and isn’t just one of those random things.
There is a theory that it dates from very early in our evolution - and I mean at the flatworm stage before our predecessors even evolved a spine. Suppose some invertebrate ancestor evolved into a flatfish-like mode of living, swimming on its side along the ocean floor. Since one eye is now pointing uselessly into the mud there is a selective advantage in the head rotating through 90 degrees to bring both eyes on top. Modern flatfish have done just this.
Later on, these creatures go back to swimming upright and the head rotates 90 degrees again to get the eyes on the sides of the head again. Since evolution is random, there’s a 50% chance that the head rotates the same direction as before for a 180 degree twist. This has the effect of causing the nerve connections from the left brain to go to the right body and vice versa, and all animals that later evolved from this creature (all vertebrates)retain this twist.
This explains why some very primitive invertebrates do not have this crossover, the theory is that they evolved before this happened.