The Golden Rule did that 1000s of years ago. The NAP does not represent any form of moral progress.
Do you live by The Golden Rule? Great! You'll fit right in in an anarchistic society. Every positive religion has a "Golden Rule," or similar. The NAP is secular, and not connected to any religious morality.
The problem is that people who feel morally superior to you and me do not "Do unto others as you have them do unto you" because they do not accept that you have the right to do "wrong." That's why government exists - without it you have people enforcing their own morality.