The reason we don't do it is because our eyeballs perceive things in perspective, not orthogonal projection. The believability of a perspective projection is much higher for the same reason that games feature humans and humanoid characters - it's what we're used to and comfortable with. A constant orthogonally projected view would get really weird after a while.
The closest we get to true orthographic projected cameras is in the isometric 2D sprite-based games like Sim City, where we didn't actually do 3D rendering, so a perspective view was impossible. It looks fine in a stylized visualization, but seeing it more realistically rendered would cause a sense of unease in the viewer, due to the expectation of a perspective view.
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