I think you're describing a level of generalization above the application at hand. We could easily train a neural network to recognize the orientation of a font, and then build an orientation invariant "reading" app by first recognizing the rotation of the text, transforming it so it is right side up, and then recognizing as normal.

I tend to imagine our brains works similarly. It's not that you have a single "network" in your brain that recognizes test from all angle, but your brain is a "general purpose" machine with many networks that work together. I think current deep learning techniques are great for discrete tasks, and the improvement needed is to have many networks that work together properly with some form of intuition as to what should be done with the information at hand.