Sounds like Imperial China's civil service exams, with emphasis on different skills. (The civil service exams focused on Chinese classics, which is probably a decent proxy for conscientiousness and intelligence but not so good at measuring social skills.)

There's obviously something to be said for the system, since it lasted for better than a thousand years and weathered several dynastic changes. But plenty has also been written about its drawbacks, and the main ones seem to revolve around regulatory capture: empowering experts to rule also empowers them to decide the meaning of "expert", which we might expect to incrementally make a system less meritocratic and more aristocratic. Goodhart's law is also worth thinking about.