Would-be rebels don't necessarily need to kill or even depose the monarch, if the monarch's power is so limited in the first place. They can just go about their business and ignore the king's objections to the contrary.

Then, of course, legitimacy itself is culturally defined, and in some places being able to depose the monarch would be ipso facto proof of said monarch's retroactive illegitimacy. The notion of "divine right of kings" is far from universal.