It is also the role of Congress and SCOTUS to check the powers the president, lest he begin to think he has the unlimited power of a king. Or, maybe he thinks that he's the CEO of USA, Inc. Of course Congress and SCOTUS are doing little check Trump's powers, so we get to sit back and have fun as we watch the chaos ensue.
The US President does have the power equivalent to a King. The reason the President plays the role of King is that the US founders were not particularly original and just took the English system of government and made some minor fixes, rightly making it into an elected King. An active commander of the nation is needed, but that commander should be the person who the populous wants to rule.
As I have posted elsewhere, the President has the power to
assassinate US Citizens at will.
The Supreme Court today ruled that presidents are entitled to “absolute immunity” from criminal prosecution for official acts, then contended that pressuring the vice president and the Department of Justice to overthrow the government was an “official act,” then said that talking to advisers or making public statements are “official acts” as well, and then determined that evidence of what presidents say and do cannot be used against them to establish that their acts are “unofficial.”
If the US President can murder US Citizens and has absolute immunity from anything he wants to do then he obviously has great king-like power. Read that article. The article also describes that it is within the President's power to overthrow Congress without repercussion. However, historically the US President has simply just ignored them rather than overthrowing them, knowing that he is above their power.
The President is the country's Commander in Chief, and is the executor of justice above the law, very similar to the role of a medieval king. Legislature can make laws, but they don't apply to him. The law does not apply to him because he is the law. The legislature is meant to make laws for normal citizens, not the President-King who has almost limitless powers.