Why was there no king in the United States at all?

There are at least four reasons why the United States never had a king. These were: the fight against George III, the theory of natural rights, the Founding Fathers and separation of powers, and the precedents established by George Washington.
Americans came to view King George III as a tyrant before the American revolution (1775–1783). After the defeat of France in 1763, the English Parliament passed numerous laws that angered the Americans. Many of these laws raised taxes, and the Americans blamed George III.
Second, the theory of natural rights influenced Americans against any kind of kingship. In the Middle Ages, kings had unlimited power. The natural rights doctrine rejected this idea. According to natural rights theory, individuals had inalienable rights. The people entered a social contract with their ruler, and the ruler had to honor that contract.
Third, the Founding Fathers did not want an executive to have unlimited power. They sought to balance executive power with judicial and legislative authorities. This is why the United States has three equal branches of government.
And finally, George Washington did not want to be king. He was so popular that he could have become a king, but he rejected the idea without hesitation. He was content to serve as first president and establish precedents for his successors.