Some great comments on my previous post.
A popular theory is that our affinity for 2D could be an artifact of the displays we are using. JeBus says: "If we had holographic technology, where the game objects actually appeared around the player in a 3-dimensional space, we'd be much better at it in-game."
But people were creating artwork and visualizing mathematics in 2D long before the invention of the computer screen! Archeologists believe cave paintings and sculptures appeared at roughly the same time. Since then, our species has devoted far more effort to creating 2D images than to carving in 3D.
I find it interesting that early paintings were not 2D projections of a 3D world, but a true 2D geometry where the third axis is simply non-existent. The idea of projecting 3D space with a vanishing point was not discovered until much later.
Beringela suggests what I'm going to call the Ender's Game theory: "We have evolved on what is essentially a 2D plane. When our ancestors hunted, they really only needed to think in 2D - how far away is that deer and what direction is it going. Its height above the ground didn't really matter."
This makes a lot of sense to me. Sure, reality is 3D, but for a species living on the surface of a planet with gravity, one axis is fundamentally different from the other two.
If this was the entire story, I would expect us to be happy to discard the vertical axis when playing a top-down game, but less comfortable with 2D sidescrollers where we keep the not-important-for-hunting-deer vertical axis while collapsing our usual north/south/east/west coordinate system into just a single left/right dimension. Yet most people seem equally at home with top-down or side-on 2D views.
DMG suggests our brains may simplify geometric problems by choosing between a variety of different projections: "We've evolved to naturally project 3D problems into 2D models. Need to find your way home to the cave? Refer to your mental 2D map. Need to hit a mammoth with a spear? Consider the vertical plane joining you and the mammoth."
That certainly matches my experience of using simplified coordinate systems for game AI.