Not the same at all, you're talking about a highly specialized skill with a small amount of people that are mostly compelled by either military order or international law. Deciding who should be the leader among the in-group doesn't require being ordained by the priesthood (the boardroom), it should be decided and voted on by the workers.

To make the actual analogy you wanted, maybe you should discuss fragging:

https://en.wikipedia.org/wiki/Fragging

And what it means when your underlings hate your leadership so much they would rather kill you than follow their "superior's" orders.

While we're at it let's get rid of coaches for sports teams and just allow the players to coach themselves

When is the last time you were someone who did real work at a Fortune 500 company and were coached by a CEO?

Just want to call out that these are both not great examples?

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.