The presidential system, widespread in Latin America, has an inherent tendency to produce caudillos. The US had the good fortune of escaping that fate for decade after decade, but maybe with Trump its luck has finally run out.
The parliamentary system, as used in the rest of the Anglosphere and most of Western Europe – it doesn't require a monarchy, see parliamentary republics such as Germany and Ireland – avoids this problem by putting greater limits on executive power – Prime Ministers derive their authority from the legislature and can be removed by it with a simple majority; while the US cabinet is essentially an advisory body to the President, Westminster cabinets are collegial bodies in which the Prime Minister is just one vote among many and can be outvoted by their colleagues.
> One of the biggest influences on my thinking from listening to Dan Carlin's Hardcore History is a point he made about hereditary monarchy, that among its problems is that sometimes the next ruler in line is just a total dud, and you're just stuck with them.
"Great Britain is a republic with a hereditary president, while the United States is a monarchy with an elective king" (The Knoxville Journal, 9 February 1896)