No identification of self or mission;
No interference with the social development of said planet;
No references to space, other worlds, or advanced civilizations

The Prime Directive, from a story telling point of view, does a very large number of things at once. It is the best example I can think of using a societies laws to help teach your readers/views about them. If you understand what a person (or people) value most, you are on your way to understanding them entirely.

First it conveys a sense of humility, of admitting that some things are beyond you. It also tells you that those who hold to it value things more them themselves and their own people. Lastly it tells you that at some point in the past they fucked up, no other reason to need to have it.

From a more meta point of view it is a VERY good story telling device because it limited the Enterprise. One of the problems they had writing Star Trek was that the ship was just too capable, the transporter alone could solve too many problems.
The Prime Directive forced Kirk and co to use more indirect means to solve problems. If they got captured the enterprise COULD just beam down 100 red shirts with phasers and get them back, but that would violate the prime directive.