I'm just trying to imagine the perception of Britain internationally when it's realised that the HOS is pretty much a mid level civil servant with no power, no perks....
I've just been reading Robert Hardman's Charles III, about the first year of the King's reign.
He describes how there was due to be a bio-diversity conference in London. Very worthy, but not at all exciting, and participating nations were going to send civil servants or junior ministers. Then someone came up with the notion that the King should host a reception at BP, and suddenly everyone wanted to be here.
Hardman talks about how, while the King can no longer personally push his favourite issues in the way he did as PoW, he can play a really valuable role as a convenor, bringing together people from all over the world to talk about all sorts of issues. He can do this because he has the knowledge and experience built up over decades, because he knows many of the people and their countries personally, and because of the sheer prestige of attending an event at a palace hosted by a King. Someone elected to serve a five or ten year term just wouldn't have the same knowledge or impact.
Similar was said regarding the Queen and the Commonwealth. She had known many of the Commonwealth leaders personally for many years, and sometimes at CHOGM, without ever getting political, she could smooth the way by having a quiet word here and there.