Well, not in the USA. The whole idea of the USA was to have a king who was reviewed every few years by a group of reliable men (the electoral college), and replaced if he wasn't doing the right thing. He could also be replaced between times if he pissed off enough senators and representatives.
This is a marked improvement on the "king for life, eldest son takes over" model, but it is hamstrung by the understandable belief at the time that somebody had to be in the role of king, doing kingy stuff like vetoing legislation and pardoning criminals.
Monarchy is a hereditary dictatorship, and dictators suck, but other models of governance are difficult to make work in a pre-industrial world, where communications are slow, and slowing things down still further by requiring discussion (which implies face to face meetings in the C18th) is just asking to be invaded and thrashed by your more nimble neighbours.
The world has changed, and distributed rule is less problematic - except for the perennial problem of how to crowbar power from the hands of the king (whether you call him King, President, First Secretary, Prime Minister, or something else).
The vast majority of us, who have zero desire to be king, need to be protected somehow from the small band of nutters, each of whom is certain that he is the only person up to the task. And they are nutters. No sane person wants to run a country.