I think most people want to be famous because:
When you are famous, you mostly have the power to influence other people. You may influence them with your thoughts and ideas and most probably, they will agree or follow.
Most famous people are wealthy. People tend to cling to those who are famous. Hence, more opportunities come to the famous people. Some people want to be like them so when they endorse certain products, people will follow which leads to them being wealthy.
This is connected to the first and second which were influence and money. When a person is famous, he or she have influence over someone which leads to wealth which leads to power. The three are connected to fame.
Those mentioned above are the factors why I think most people want to be famous.