think this natural assumption comes from the ancient idea that the eyes are the 'windows or doors of the soul' through which the soul 'looks', or 'goes', out into the world and brings back the objects into itself. — John

Also, it just seems that way as a matter of experience. It appears that I am looking out at the tree as I walk by it, not that light from the tree is hitting my retina in 2D, upside down, where my brain has to right it, infer the depth, and put me into a visual space that coincides with my walking motion, what I'm hearing, etc.

Yes, true that! I mean, the fact that it seems the way you outline probably explains why the idea of the eyes as windows of the soul arose. If it had seemed some other way, another kind of notion would have arisen instead.