While we're at it let's get rid of coaches for sports teams and just allow the players to coach themselves
High performance sports teams have a captain that is often elected in some form from the team.
Likewise the crew of a pirate ship used to elect their captain.
Both examples serve contrary to your point, and there's no reason you couldn't have something similar in business: a cooperative that elects a CEO, rather than it being done by a board of other CEO's.