An "elective monarchy" is actually a kind of interesting way to describe the US system, I think.

The presidency as it is set up in the USA is an extremely powerful executive position...moreso than is the case with most prime ministers in other western parliamentary systems. Thus it is seen in many other societies as being a rather imperial office in its nature...but one that is limited to only 4 years...then subject to re-election...then limited to only 4 more years. In that respect it is like a parliamentary monarchy which is subject to renewal by election at given intervals.

Remember, monarchs are not necessarily absolute rulers, not by any means. The British monarchy, for instance, began having its powers limited from the time of the Magna Carta on...and this necessitated negotiation on the part of the monarch with what became the British parliament.

In the Hundred Years War, for example, the British kings of that era had to go to Parliament to secure funding and approval for their foreign military adventures. Sometimes they got it. Sometimes they didn't. They were not absolute rulers.

And that was way back in the 13 and 1400s!

The American revolutionaries of 1776 were not rebelling against an absolute monarchy, they were rebelling against a distant colonial regime run (inefficiently) by a parliamentary system with a monarch as the titular head of state...and the problem was that that parliamentary system and the monarch were out of touch with some of the fundamental aspirations OF the American colonists to the extent that they screwed up their administration of those colonies and lost the loyalty of a fairly narrow majority of the colonials in the process.

The presidential system that the Americans installed after their successful revolution had been achieved was built around a chief executive that had rather king-like powers in a number of ways, and it's hardly surprising that a lot of people wanted to crown George Washington the first king of the new country upon achieving independence from Great Britain! (Washington rejected that idea, however, much to his credit.)