Matt Yglesias makes it implicitly, Royal Wedding and the Case for Monarchy:
The point here is that it seems inevitable in any country for some individual to end up serving the functional role of the king. Humans are hierarchical primates by nature and have a kind of fascination with power and dignity. This is somewhat inevitable, but it also cuts against the grain of a democracy. And under constitutional monarchy, you can mitigate the harm posed by displacing the mystique of power onto the powerless monarch….
If humans are superstitious and collectivist by nature (which I grant some would dispute) then the same logic would apply to an established religious order. Something innocuous such as…the Anglican Church?