i don’t actually know this, this isn’t a rhetorical question, but, like, do other representative democracies expect that their heads of state maintain 14-16 hour a day, 7 day a week schedules, or is that just specific to our national obsession with looking busy?
From what I understand it's function of our President be an executive with a capital E, the Prime Minister of the UK, for instance, simply has a lot more bureaucracy and shares a lot more power with Parliament.
I mean “head of state” means functionally a lot less when winning an election more or less automatically appoints cabinet positions. The parliamentary system vests most power with parliaments.
there's an entire category of things that head of state does and head of government doesn't. functionally we do devolve a good chunk of that to other proxies, but our system is somewhat rare in that head of state and head of government are the same person.
you obviously can manage to get by with them being the same person-- we have-- but there are good reasons (not always the same good reasons) why most other systems don't.
To me, the most interesting set up is independent countries that used to be part of the British Empire (e.g. Canada and Australia) that continue to use the British Monarch as the Head of State via an appointed Governor General.