Look at how its going with the EU, which is the closest thing we have to this kind of nonsense.
Who is the current President of the European Commission? Ursula von der Leyen - by common consent one of the most incompetent politicians of the time, in charge of Germany's defence and had soldiers running around with broomsticks because she couldn't supply enough guns. And how did she become President of the European Commission? Did she win an election against some other terrible Eurocrats? Did she come second and then somehow got appointed like the horrendously awful Rishi Sunak? No. She wasn't even in the race. They had an election under established EU rules, which she was not a candidate in. Manfred Weber won more seats than Franz Timmermans and should have become President. Instead, the European Council simply decided to annoint a completely different person (von der Leyen) as President, subject to a confirmatory vote, in which she was the only candidate. She very nearly lost that one-horse race. It would be like having a General Election here, Starmer winning more seats than Sunak, and then Holly Willoughby becoming PM the next day.
That should tell you exactly how the position of "World Leader" would be appointed.
As to how it would work in practise - simply look at the UN. Utterly corrupt and utterly incompetent.