As a neurologist myself, I was taught it was specifically to simplify visual processing, although there may be other theories but this is what I was taught. Like others commenting here, the way the lens works in each eye is by flipping the image onto your retina. If we had only one eye, there would be no issue, the image would appear as a continuous image, just flipped around. However, because we have two eyes, they both individually flip different fields, thus separating the continuity of the image horizontally. If you try drawing out various different ways to try and remedy this problem of binocular vision, the way nature's approach is quite elegant in reuniting the image as well as separating visual processing into left/right.
To avoid a large text explanation, this is a simple diagram of the concept how the brain reforms the arrow. https://nba.uth.tmc.edu/neuroscience/s2/images/html5/s2_15_1...
The way it works is by separating the left and right fields of each eye, and then crossing them so that the left fields goes to the right half of the brain and the right fields go to the left half of the brain. Each right/left half is now interpreted by one side of the brain and the image is again continuous if you draw it out on the brain. Of course now each side of the brain sees the opposite side, but we remedy this by crossing everything else so it plays well with visual interpretation. Now the right side of the brain sees, senses, and controls the left side of the body and vice versa.
When it comes to everything else, there isn't a clear benefit for having processing swapped to opposite hemispheres. But visual processing benefits from it greatly, and so the rest of the nervous system goes along with it.