Nobody, no matter his title, shall ever be untouchable and self-controlling. NEVER. Thats why we have balance of powers in the West, and just those who want unlimite dpowers try to erode and corrupt this system (quite successfully, unfortunately). In my best understanding, a US president is not meant to be a monarch, though much symbolic stuff in the representation show act of the state and its pomp and also the president's ceremonial acts and public perception of him remind of the monarchy (that the colonists threw out of the window, mind you...).
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If you feel nuts, consult an expert.
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