In the rare cases where they do want to change the government, most of the time, they will think, Bring back the old ways.
Witness how few people are calling for a monarchy in the United States. Even a Constitutional Convention is on the fringe. And in Europe, those who want change generally call for dissolving the European Union, reverting to the previous national structures.
They do have a point. What's the point of shifting around the governmental structures when the fundamental problem is that they are built of human beings? And an old governmental structure must have worked, for some value of the term "work", at some point.
Deposing the king can get icky. (That's a technical term, there.) Which is why they tend to denounce his evil councilors, his favorites, his mistresses -- sometimes his queen, though that can get tricky. But it does depend on the exact theory of kingship. In some times and places, deposing him is even the right of the -- people, or council, or something.
But those who want reaction, even, are fringe, and those who want revolution are nutcases in an overwhelming number of societies.