Nerves do regrow, but not from the spinal cord as I understand it, and just because they regrow does not mean they regrow along the path which is needed to repair function.

My father broke his Bricial Plexis (the nerves running through your shoulder to your arm). There was an 18 hour surgery to re-trace the path for the nerves to grow. Some nerves made a connection, and he has minimal movement in his fingers. However, most of his arm is still paralyzed.

I got the ear nerve almost severed as a kid and I am still 100% deaf from that ear, it's been 30 years already.