I have been working for a fast growing/successful startup that has brought in a number of outside executives (though not a new CEO). I am sure those executives have 100x the stock of the average engineer on the team.
These executives get paid the big bucks because a) they are scarce and b) their job has way more leverage than the job of an engineer.
The nature of hierarchies is that there are fewer people at the top. Thus the number of people with a proven track record as executive is always much lower than the number of engineers. Thus there is a small pool of executives for a company to hire from.
It is worth it for a company to pay top dollar for proven executive talent, because an executive has 10-100X more leverage than that of an average engineer. The old line is that engineers can differ in productivity by orders of magnitude. Well, the executives determine which engineers you end up with. So the difference in executive talent is that order of magnitude times the number of engineers. The executive determines how well they the team works together and how much distraction and interference the team gets from the forces of entropy and chaos that surround the department. We have hired outstanding executives that have brought their divisions to new levels. We have hired bad directors and VPs who were disastrous and were fired. In some cases, a person who grew up with the company did not scale, and had to replaced. In other cases a person has risen with the company and taken on enormous responsibilities.
I'm guessing that the outside executives brought in at a startup that is struggling are on average much, much worse than the outside executives we have brought in. After all, the good executives will opt for a position at the company that is growing fast. Who wants to try and save a sinking ship?