Okay, I'm gonna get to my point: My thesis is that his pay is not actually meted out in a way that related to his contributions. It's an artifact of incredibly limited access to being considered for the position, and of the power a CEO wields. Not skill, not contribution to the company: Just raw power that comes with the position.
A CEO needs to be paid large sums of money enough to encourage them not to make corrupt, self-enriching decisions at the expense of the company; Also a CEO has a personal relationship with the people determining his salary and has the ability to arbitrarily ruin them/their company. Also there is some unwarranted hero worship in humans views on things: Board members, and people in general attribute success to a specific CEO much like they attribute an entire movie to a specific director, without consciously taking stock of the contributions of support staff.
The first one, yeah we're not going to be able to do a lot about. We don't want our CEOs trivially bribe-able. Still, I posit that's achievable with much smaller sums, and it may be possible to instead just be more aggressive about replacing corrupt CEOs. Anyways.
I'm going to go one level further and posit that CEOs are nothing special, in an additional argument that is easy to argue with me with because it's a more speculative argument.
Imagine there was an objective, computer-system-aided HR department that accepted applications for CEO of McDonalds and reviewed them in a similar way to how the review applications for a mid-tier software engineer position. Skills and education are considered, there's an interview, functionally no nepotism, and, importantly, the review accepts applications from the general public rather than an extremely limited pool of pre-selected candidates based on the biases of the board and who they've 'heard of' already. For every decent software engineer position at a good company, there are often hundreds of extremely skilled applicants. Absurdly skilled, motivated, driven people who get top marks. How many people would apply to a CEO position, even at low salary? At an 80k salary, say? Maybe 120k? It's interesting, challenging work that can impact the world. You'd get super heavy competition from very impressive, very smart people, and they would be replaceable by any number of similar, skilled people that also want the job. There's nothing special about CEOing that is so much harder than every other job that they can only be run by irreplaceable geniuses; Their 'irreplaceable' rock-star image is artificial. They are an important cog in a corporate machine, just like having a skilled head of accounting or a good software developer.
This last set of points is a really shaky hill to die on though, I realize.