I don't know the right answer here, but there are thousands of public companies. If every CEO has to be a celebrity, meaning that everybody knows them and which company they are the CEO of, it's going to end up like for actors: tier one world superstars, tier two stars, then people you don't hear much about, then people you read their names sometimes in the closing credits, otherwise they are only random faces on screen.
If that's the case, the top layers of the system have space for so many CEOs. Some won't even care to be there, they'll just do their job and take the salary plus bonuses.