Well it seems you doubt the science behind depth perception.
Lack of depth perception or even poor depth perception can disqualify one from many pursuits. How many one eyed pro tennis players are there? How many pro baseball players are there?
When I was involved in film making one of the subjects we studied was forced perspective. On standard 2D film which is equivalent to looking at a scene with one eye we could make a frog look to be bigger than a house. No one who was actually there with both eyes open would see it that way.
If you've convinced yourself that you can see just as well with one eye as with both eyes far be it from me to disabuse you of that notion.
There are actually people who are totally blind, some with no eyes at all, who are convinced that they are not blind. This is called "Blind sight". The auditory , olfactory and other senses are routed through the visual cortex and in their mind they see images and scenes that correspond to that sensory input. Not accurately of course but they are convinced they actually see no matter how many times it is proven to them that they can not.