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.
Very few individual employee firings will have broad impact on the company the same way a CEO firing will. The whole process is disruptive by nature, so a board needs to be sure.
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.
Cultural practices exist for a variety of reasons. This is one of them. The people in the ownership class need each other for various reasons because they have control over substantial resources than can disrupt the plans of other members. For lower level employees, their only strength is numbers and unless they realize this they can be treated much worse for arbitrary reasons.
It sucks but to interface with elite culture and get them to give you money, it helps to have members of that culture as your leadership. Otherwise the non-elite wouldn't even have jobs (which are not needed so badly by the elite).
My immediate thought is that this is due to visibility. You can churn through the lowest level positions for a while before questions are asked, but you can't do that for CEOs. Its also the case for other prominent positions. If someone with a big following joins and then leaves very quickly someone will comment on it and if its big enough an article will be written. No company wants to be noticed for people leaving, but they'll make a big song and dance when big wig from X company moves to them.
I am not a media person, a board member of a major company, nor an executive. I am a socialist, so I find it simple to express the sentiment of class war that is so anathema to the elite classes that partake in it constantly against the lower classes.
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.