Sortition has lots of upsides. Given the US doesn't really have an obvious source for a Monarch (which is the definitively best way option), using Sortition to fill the Figurehead role would be a good solution.
The other half of the job currently named "President of the United States of America", heading the Executive function, would naturally make more sense as a route for either state leaders (e.g. Governor -> President) or the legislature (House and Senate leaders -> President)
It should definitely be prohibited for one person to have both jobs as is done today. Donald Trump would make a perfectly good figurehead. The world would say yup, that's what we thought, a fat idiot who flashes his money and talks crap, America. Meanwhile the executive leader would negotiate say, tweaks to agricultural tariffs and that'd go largely unnoticed because e.g. now the buffoon is pretending "everybody" thinks Belgium is in Africa because he refuses to own up to mistakes and that's way funnier than China reducing some agricultural tariffs.
The US would need to do a LOT of paperwork to make this happen though and a remarkable, disappointing fraction of Americans believe that their existing paperwork is sort of holy and mustn't be changed even though it was written in an era which is unrecognisable socially and technologically. So you're probably screwed.
> a Monarch (which is the definitively best way option)
What metric are you using that demonstrates that a monarch is definitively the best way?
> It should definitely be prohibited for one person to have both jobs as is done today.
Why?
> Donald Trump would make a perfectly good figurehead. The world would say yup, that's what we thought, a fat idiot who flashes his money and talks crap, America.
Ah, so the reason monarchs are the best choice for figurehead is that it's inherited, so on the one hand you have a good heads up about future figureheads (you know there's a good chance from the moment of birth who it'll be) and can ensure they're properly trained for this role, learn some world geography and history for example, practice meeting random people and at least pretending to be interested -- but on the other hand nobody can control who they are, that's just the result of a genetic lottery.
As a result they also have zero democratic legitimacy, which is good because obviously as figurehead they'd otherwise be in an excellent position to seize actual power, which is the last thing you'd want to happen.
As to why prohibited, the temptation is, as you see in the present job of President of the United States to combine the two. Rather than ask people to resist this temptation, just prohibit it up front. These roles are huge asks, in terms both of the skills needed (or at least which ought to be needed) and the burden of responsibility. It would be easy to underestimate the figurehead role in particular, but it just isn't easy to be a symbol for hundreds of millions of people. So, de-risk by insisting on two people for two roles and never merging the role.
This is a cogent argument for having a ceremonial and practical/executive head of state, but doesn't even touch on why a hereditary monarch is in any way superior to having a ceremonial President and executive Prime Minister, as is common in other countries.
The monarch plainly has no legitimacy whatsoever, there's no merit, nobody elected them, they were born into the job.
In contrast an elected President can use the ceremonial position to seize actual power. This isn't even just theoretical, it's an actual problem - or I guess if you've just used it to seize power, a brilliant feature...
Anyway, we don't want that, so the monarch is better.
The other half of the job currently named "President of the United States of America", heading the Executive function, would naturally make more sense as a route for either state leaders (e.g. Governor -> President) or the legislature (House and Senate leaders -> President)
It should definitely be prohibited for one person to have both jobs as is done today. Donald Trump would make a perfectly good figurehead. The world would say yup, that's what we thought, a fat idiot who flashes his money and talks crap, America. Meanwhile the executive leader would negotiate say, tweaks to agricultural tariffs and that'd go largely unnoticed because e.g. now the buffoon is pretending "everybody" thinks Belgium is in Africa because he refuses to own up to mistakes and that's way funnier than China reducing some agricultural tariffs.
The US would need to do a LOT of paperwork to make this happen though and a remarkable, disappointing fraction of Americans believe that their existing paperwork is sort of holy and mustn't be changed even though it was written in an era which is unrecognisable socially and technologically. So you're probably screwed.