> [...] and elsewhere kings are usually coronated by the Pope of the Catholic Church.
Only in catholic countries. I haven't looked up the numbers, but I assume less than half of remaining monarchies are catholic. Mostly because we have a number of protestant monarchies (like the Netherlands and Denmark), and we have plenty of monarchies that aren't Christian at all (like Thailand or Malaysia or Saudi Arabia).
That's why I specified "usually", not all kingdoms are Catholic or even Christian but I would presume most would have similar concepts of deriving authority from somewhere to claim their blood is blue.
I'm not sure, but what you claim seems plausible enough.
Republics typically also make these kinds of claims to legitimize their leaders' claims to power. They usually invoke the wishes of the people or even a 'general will' (https://en.wikipedia.org/wiki/General_will).
Only in catholic countries. I haven't looked up the numbers, but I assume less than half of remaining monarchies are catholic. Mostly because we have a number of protestant monarchies (like the Netherlands and Denmark), and we have plenty of monarchies that aren't Christian at all (like Thailand or Malaysia or Saudi Arabia).