Boards hesitate to remove CEOs but CEOs don't hesitate to remove employees. Elite culture requires social niceties and soft treatment while everyone else gets scored, disciplined, and underpaid.
This isn't just "elite culture", although there is probably some of that in many scenarios.
edit: responding to a couple of comments - yes this is a feature of how we choose to structure these companies, it is not unavoidable. However, given the distribution of decision making and responsibility in a typical American corporate structure, removing the CEO is inherently difficult.
One can imagine situations where it is less disruptive, but those companies would look and operate quite differently.