I'm a long-time SF reader, and such ideas have already been explored - and I might add, without any obvious flaws emerging (which proves little).

Frederik Pohl wrote a criminally underappreciated collection of short stories called "The Years of the City" about the future political history of New York City and America. Anyone who is interested in better systems for decision-making should read that book.

In particular, the story "Gloria and the Supremes" zooms in on one woman who is a Supreme Court justice - which means she is a random person selected out of tens of millions who are eligible by not being criminals, passing various tests, and such, and then given a staff of actual lawyers.

Arthur C. Clarke is always an entertaining writer - his "Imperial Earth" is a little less thrilling than his earlier work, but still a decent read. In that future, it is possible to mechanically read at least some things about what humans want and believe - and political leaders are chosen from a pool of responsible people who do NOT want the job, on the theory that anyone who wants to order people around is a psychopath!

You get to see a little into the mind of the World President, who's hoping that if he handles the crisis well enough, they will let him quit and go back to his academic studies, because you get time off for good behavior.

If our civilization is to survive the next century, which I confess seems impossible at this instant, we will have to dramatically improve the quality and honesty of leadership.

Yes, America is the obvious example, but I now live in the Netherlands, and our leadership here, though of course not as bad as the execrable Trump, has completely muffed COVID, and refuses to apologize, admit blame, or change their reckless course.