Science Fiction Aficionados discussion

This request is from a friend. I have not read it myself, but he gave enough detail to make a positive identification. So, here goes:
He read the book 30 years ago in paperback. The story is about a post-WW3 world. There is some sort of automated defense system left over from the war that shoots down anyone attempting to fly an airplane. The humans on the ground live as savages, slaying "dragons" (actually robot tanks) to make crude weapons from their "skin" (armor) and jewelry from their "guts" (electronics). Humanity has mutated somewhat. The hero is a savage, but has retained the now rare and derided trait of having facial hair. My friend distinctly remembers the phrase "scrape the shame off his face" as the hero shaves.
There are also humans in space who kept their technological society but can't land or even enter Earth's airspace due to said defense system. The hero at some point enters an abandoned silo from the war and manages to turn off the system, the space-humans land and happy ending ensues.
So, does any of this sound familiar?

Could it have been a short story? This sounds familiar to me, but what I am thinking of is a short....

nope. It was definitely a paperback novel.