Ideally, yes, but some Kings (or the equivalent) do neither. Or, if they abuse their people, the whole thing eventually crashes violently, in most cases.
I’m not saying it (monarchy) can’t work, I’m just saying that giving rulers immunity, or perceived immunity, is more often than not a sure recipe for big trouble. Immunity corrupts, and those “outside” the power circle feel they have no voice and no hope, therefor they usually turn to violence. 1776.
Who said anything about immunity? The monarch has an obligation to the people. The people have an obligation to the monarch. His “immunity” is a set of contractual obligations, not unlike what you have with your colleagues and neighbors.
Monarchies go bad, usually when an infant succeeds to the throne or the elderly king becomes incapacitated, and the regents form a little democracy around him. But monarchies go bad due to something extraordinary; democracies go bad because they are designed to go bad.
King George III was a remarkable king for his country, Britain, which he lead to dominance through very turbulent times. In fact his reign was quite illustrious: he really was the first national king in the line of Hanovers; he formed a union with Ireland; successfully outmaneuvered the Parliament — which gave him great popularity among the people; he, ahem, ahem, defeated Napoleon. He was loved by Britons for his exemplary family life and piety. It is a cruel twist of history that on American continent he is only known as a mad tyrant.
1776 was a birth of the American Nation (very similar to the Maidan today). Monarchy does not work very well across distance, precisely because the intimate bond between the king and the people cannot form. American independence was a natural consequence of this; to elevate it into some universal social principle of republicanism is illogical. All colonies sooner or later reach independence because they become nations. Then they choose their form of government; typically they call in a prince not unlike when a young woman finds a husband. American experience is not a universal pattern, and given the Revolutionary War, the 1812, and the Civil War that attended our birth, it was not particularly bloodless one.