Thinking about 3D

Here's a thought. Did you ever notice that 3D films and photographs, although quite stunning, never quite look like the real thing? They always seem to look a bit like one of those diorama things made out of layers of cardboard cutouts, or a theatre set. Why is that?
The answer must be that neither film, nor photograph contain enough data for the brain to create a true 3D image, as we experience them in real life. This seems strange because, if you know anything about 3D photography, you know it's all about recreating the way our eyes see. The 3D effect is made by using two cameras: one to create an image for the left eye and one to create one for the right. Once these two images are created, you need some kind of viewing device to ensure that the correct image to delivered to each eye. (Modern movie systems use polarised light and glasses, Victorian photographers used a piece of cardboard, which you place between the pictures at right angles and held against your nose.) Normally, the two cameras are placed the same distance apart as human eyes, but by moving them closer together or further apart, you can create perspectives which give an illusion of being either larger or smaller in relation to the scne being photographed. It's a lot of fun, but it doesn't quite work.
I figured I knew how to fix this and how to make it work for live sports TV or news coverage, but I needed to check with my son to see if he thought I was right.
If I was right, it ought to be possible to recreate the false 3D diorama effect by using our eyes alone.
My son was successful, but I couldn't get it to work, no matter how hard I tried. I still had a hunch I was right, though, because I could feel my eyes moving about like crazy. My son pointed out the problem. We were each facing in different directions. In his field of view, the room was clearly defined into a series of planes by the wall, the TV, the unit the TV was standing on and a coffee table with a mug and glass. I, however, was looking at a setteee with a confusing junble of cushions and blankets, compressed into a relatively short distance. By exchanging places with my son, I was able to confirm that my idea was a good one. The diorama effect is caused by a static perspective.
When we look at something in the real world, our eyes are constantly scanning over it, moving about and sending data sets from different perspectives. Because our eyes are also able to send data about their own movements relative to the viewed object, our brain is able to construct a complex 3D image, where this is desired. The reason I was unable to create a diorama effect by not moving my eyes was that the object I was viewing was too complex to create a diorama which would make any sense. Trying to do so only compelled me to move my eyes. My son's perspective was more successful because the relative positions of the objects could be usefully interpreted in the form of a diorama.
I'm guessing that we normally see a lot of the world in diorama form, any way, which is why 3D photography works at all. It is only when we want to view 3D detail, that multiple perspectives become necessary. The reason we notice the diorama in 3D film is because, when we try to get the detail, it isn't there, because moving our eyes doesn't change our point of view.
This is a particular problem for sport, where we will very often want to untangle one footballer's leg from another or predict who is going to get the ball.
The trick, then, is to make sure that moving our eyes DOES change our point of view when we are watching 3D sport at home. That's a pretty easy problem to solve, isn't it? Particularly when, by changing the distances between the cameras, you can make the view go really close to, or really far away from the action.
Can't think of a feasible way to make it work for recorded footage, though.