One thing I don't fully understand is why the human body doesn't do this process on its own.Indeed. Furthermore, it seems that there is an inverse relationship between how "advanced" an organism is in the phylogenic tree and its ability to regenerate--especially to regenerate nervous tissues.
One of the major cutoffs seems to be between mammals and other vertebrates. Frogs and amphibians can regrow their nerves if they are cut or damaged [1] and fish can completely regrow their cochlear hair cells, regaining hearing in a mere matter of weeks following deafening from exposure to very loud sounds [2].
The "reason" for the loss of regeneration in mammals could have something to do with the fact that mammals are more able to undergo plastic changes to their existing neurons (learning new skills, for example) at the putative cost of being less able to regenerate new cells. Ultimately, being able to learn and exhibit complex behaviors may be much more evolutionarily advantageous than being able to regenerate damaged nerves.
1. There is actually a clever experiment you can do using this knowledge. You transect the frog optic nerve and rotate the orb of the eye upside-down. Then you ask the question: will it reconnect as before, with each axon in the nerve fiber reconnecting to its now rotated mate and the frog consequently now seeing the world upside-down -or- will each axon reconnect to the closest axon (which would have originally been the incorrect one resulting in the frog still seeing the world the right way up? The answer is that the frog acts as if its vision is inverted, providing evidence for chemical signals being used to guide nerve regrowth. As an aside to this aside, note that people and most mammals can adapt to prism glasses (glasses that invert their vision) in a matter of hours. Amphibians, however, will never learn to use prism glasses no matter how long you let them practice.
2. There is work underway to identify which genes are responsible for allowing fish to regenerate their hearing with the ultimate hope of being able to transiently "turn on" the human gene homologues.