alt Hacker News"for all practical purposes"
Well, there is the practical purpose of legitimacy. It may seem too soft for modern power theoreticians, but the legitimate king has something that cannot be acquired by raw power, and that puts somewhat of a damper on potential rebels. Not on each and every one of them, of course, but it has a wide effect. Killing or deposing the legitimate monarch was a serious spiritual crime for which one could pay not just by his earthly life, but in the afterlife as well.
Even usurpers like William the Conqueror tried to obtain some legitimacy by concocting stories why they and nobody else should be kings.
We still see some reverbations of that principle today. Many authoritarians love to "roleplay elections", even though they likely could do it like Eritrea and just not hold any. It gives them a veneer of legitimacy.
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.