Yes, star power is necessary in diplomacy, because diplomacy is selling your country and its interests, just like selling any other good or service is. People are more likely to agree with your position if someone credible says they should agree with it. Sending important people also sends the message to the country that we think they are worth our time.
In diplomacy I believe that it is important because you need someone that is going to influence any type of good recommendation going your way, you dont want someone who is a negative character in on your diplomacy because they may give the people a bad vibe of you and what you represent.
I do not believe star power is necessary in diplomacy. I believe these situations are best handled by the people who are most knowledgeable about them, not the people with recognizable names. Diplomacy has nothing to do with star power, you wouldn't send Matt Damon in to discuss human rights, just because he's a popular face.
No, there is not a thing that says that you need to have star power. The people just have others that they make famous and like watch and be entertained by, so there is always stars that are out there, but they are not by any means required in the world.
I believe that in the United States Star power is not a necessary thing when it comes to diplomacy. Though often people like the idea of star power it is not always what is best for the majority of people. Often times star power is used to throw money and power around to get ones ways even if it is not in the best interest of everyone.