Because, the USA is a very federal country and there´s little a President can do to change the way America is going other than by convincing Congress, Governors and Mayors to go along with him.
Because, the only area in which a US President really has power is in the military and foreign policy.
Because, the EU, which could be a true military rival of USA, not in the sense of enemy but in the sense of forcing USA to act in sync around the world, doesn´t really have a post WWII vocation for the role.
Because, China is not there yet.
Because, the UN is ineffective and little countries have an absurd amount of power. The UN never came up with the Senator/Representative solution to distribute world power. It either has the veto concept by very few countries that are too powerful, or it has the one vote per country that gives little countries too much power.
Because, America is the biggest global exporter of culture and most movies – TV shows do a great job at promoting the image of the US President around the world.
Because, the authority of the US President is so resilient that not even George W. Bush was able to destroy it. Bush had a significant chance to improve the state of the World and he did the exact opposite. He inherited a world mostly rich and mostly in peace and he and his administrations made such wrong decisions that the world is now less rich and less peaceful. Obama has a chance to change the course.