What if someone like the mad Roman Emperors Caligula or Nero became President of the United States?

Given that three Presidents have been impeached in the U.S. in the last fifty years, this wouldn't seem to be too far a stretch. In fact, I suspect that currently many Democrats would perceive Caligula or Nero as rather enlightened and temperate leaders, in comparison to Donald Trump. There could also be comparisons made to John F. Kennedy, although he didn't live long enough to ever be impeached. A pertinent question is the extent to which Caligula and Nero, in some ways the "gold standard" for insanity, historically speaking, really were "mad". Bear in mind, most of our information about their reigns comes from members of the Senatorial class like Tacitus, who thoroughly detested all the emperors because they were displacing traditional Senatorial powers. For example, Nero was ridiculed for castrating and publicly marrying his favorite slave boy -- in contemporary terms, he would seem to be a great early champion of LGBT rights! Caligula was attacked for claiming Imperial divinity, but the Divine Right of Kings has turned out to be a very fundamental principle in all Monarchial forms of government. Caligula, although often portrayed as being totally insane, never really faced any significant popular dissatisfaction, at all. His brief reign was actually rather successful, in military and social terms. He was murdered by a conspiracy of Nobles and the Military who were unsuccessfully trying to reestablish the Republic, and were dissatisfied with Caligula's demands for increasing Imperial power. Actually, we probably have already had U.S. Presidents like Caligula and Nero.