Why is the U.S. the central player in the Middle East?
The main reason is power. By the time Israel was created, with the end of the British Mandate over Palestine, World War II was just over and the European powers, victors and losers alike, lay decimated by war. Of all the major powers, only the U.S. survived the War intact and with economic and military power on the rise.
The U.S. spent the Cold War years locked in contention with the Soviet Union, as much as anywhere else vying for influence in the strategic Middle East. With the end of the Cold War, the collapse of the Soviet Union, and the U.S. victory in the Gulf War that profoundly altered the Middle East in favor of even greater U.S. influence, Washington's now-unchallenged super-power status only expanded. Today the U.S. remains the controlling authority in shaping the political map of the region.
The combination of the U.S.-Israeli "special relationship" and the vast superiority of Israel's power in the region further consolidates the U.S. centrality. As long as Israel remains the strongest military force in the region, with the fifth most powerful nuclear arsenal in the world and one of the most powerful conventional militaries anywhere, other countries in the region and around the world will tend to limit their diplomatic imagination to what they think Israel will accept. That means acquiescence to continued U.S. control.