Let's be honest: fear is a great motivator. The fear that you'll fail your Calculus midterm, the fear that your friends won't like your haircut, the fear that your FB status update won't be funny enough to get "Likes"… yeah, fear drives a lot of what you do. Same in "The Nose." Fear of being inadequate, fear that your drive and ambition are still not enough to outperform a fiercer rival, fear of literally losing your manhood or figuratively being castrated, fear of making a fool of yourself in public. Whew. We're feeling a little anxious ourselves. What's more, although each of these fears is represented through Kovalev's interactions with his nose, they each have a more realistic form as well. For example, the ambition of the nose only matches the ambition of Kovalev's higher-ranking friends; while his sexual fears are pretty clearly based on the fact that there's a rival for Mademoiselle Podtochina's hand in marriage.
The nose is a better, less fearful version of Kovalev. It's really just trying to show him the man he could be if he lost some of his hang-ups.
The point of the story is that fear is the glue that holds society together. Take it away, and you've got rogue operators like the nose heading for total domination.