Also, the American way of life is so universal that our constitution can be recreated by human like aliens who know nothing of Earth WORD FOR WORD. So according to Gene Roddenberry, American humans are the most important "thing" in all of existence.
Makes sense, being Roddenberry was American and all.
The Constitution is based on universal principles, freedom. You aren't going to base the Federation on Sharia Law, or some other oppressive society Also, the history of America has also shown us how we can improve ourselves, we learn from our mistakes. Plus the original Star Trek mirrored society. The Federation was "the west" (USA), the Klingons were the Russians, and the Romulans was "the east", China.