At that level, you don't get the salary your work "is worth", because we all know that's a fictional concept. Dollar value is only well defined for finished products. For labor, it comes down to relative leverage, and as a CEO, you get whatever you can get, and your buddies are on your board and you're probably on their boards, so usually that number is quite high.
CEOs may not be smart in the IQ sense we nerds tend to worship, but they understand leverage and positioning, and they understand how to hack complex human systems for personal benefit, because it's what they did to get their careers in the first place.
I'd probably argue that's an extreme example but, yes, many CEOs absolutely do make a difference in terms of establishing culture and setting direction and strategy. Certainly bad CEOs can do a lot of damage. And I expect a lot of people saying CEOs don't make a difference would be utterly lost if they were dropped into the position at a large company.
CEOs may not be smart in the IQ sense we nerds tend to worship, but they understand leverage and positioning, and they understand how to hack complex human systems for personal benefit, because it's what they did to get their careers in the first place.