So what's the reasoning behind that?
The grand European theory has been that it arises out of the nature of Man, to congregate in families, and for those families to join and form society, which needs to be ordered by the state, which derives its authority from the order and peace it provides to the commonwealth. So Burke argues:
We thought, Sir, that the utmost which the discontented Colonies could do was to disturb authority; we never dreamt they could of themselves supply it--knowing in general what an operose business it is to establish a government absolutely new. But having, for our purposes in this contention, resolved that none but an obedient Assembly should sit, the humors of the people there, finding all passage through the legal channel stopped, with great violence broke out another way. Some provinces have tried their experiment, as we have tried ours; and theirs has succeeded. They have formed a government sufficient for its purposes, without the bustle of a revolution or the formality of an election. Evident necessity and tacit consent have done the business in an instant. So well they have done it, that Lord Dunmore--the account is among the fragments on your table--tells you that the new institution is infinitely better obeyed than the ancient government ever was in its most fortunate periods. Obedience is what makes government, and not the names by which it is called; not the name of Governor, as formerly, or Committee, as at present.
Which means that the government in charge derives its authority from that very fact -- and puts rather a damper on the thoughts of the long-lost king from the old dynasty.
The problem with that is that many a king is discontented with the thought that he's just as good as -- but no better than -- any other form of government, and any other king, provided they are as just. And he does have a point, insofar as that theory does tend to create a temptation to institute a new government by violence, since it would be just as good. The Chinese framed their theory of how dynasties succeeded each other on it, but their history was never quite so neat as before it got smoothed into the theory, with plenty of cases where the old dynasty wasn't half so corrupt as claimed, or the new one half so skilled at getting all the power into its hands.
Logically, the new government would have to be not only as good, but better enough to justify the necessary wrongs that will occur during the overthrow, though that does tend to be little considered. Your own grievances always look bigger than anyone else's. There are those who would just go for a power grab, but then, they tend to be unmoved by such considerations anyway.
Though they may be moved by others. Which is yet another reason to hedge about the king with more manifestations of authority. All that pomp and circumstance and spectacle, dressing him up in purple and sticking a golden crown on his head. It impresses people. And the ceremony with religious trappings, coronations especially. The Lord's Anointed -- wouldn't it be dangerous to strike him down? And because he's the one appointed by God, wouldn't the next government be worse? Emphasizing how old it is and how custom has lasted for centuries also helps, even if the king has it made up or at least embellished.
There would always of course be those who took his existence as being as fundamental as the wind and sun. Witness those who think that democracy ought to be instituted everywhere at once, ignoring the many spectacular historical and current day failures, and apply to all governments general. . . . This is a problem with people reading Julius Caesar, who often think that the assassins were doing an Obviously Good Thing by killing him, but while Shakespeare has no mercy on usurpers, there was no one on the throne of Rome. Given that he lets Caesar's ghost haunt his killers, it's not exactly a foregone conclusion that he disapproved of taking it then. (And any familiarity with the history of the later Republic and earlier Empire shows that it wasn't in real life a bad thing, in terms of the peace and order of the commonwealth. Though Augustus called it reviving the Republic, not being a fool and wanting some of that ancient authority for himself.)