I think it's about risk aversion and social proof. The CEO can usually persuade the board that they're important, and the board can easily pay them a lot, so why not do so, rather than risk them leaving? Once enough boards do that, it becomes the "going rate for CEOs" i.e. social proof / herding takes over.
Also, the aforementioned difficulty of measuring CEO performance perversely becomes an asset. When people don't know the quality of what they're buying, but they feel that quality is very important, they'll turn to any proxy (Harvard on resume, butt was in chair while previous company was doing well) and pay top dollar for that. You can't pay for quality, but it's extremely easy to pay for scarcity if you really want to.
It just comes back to... if you have a lot of money to spend, and the purchase might matter, you'll often be willing to spend a lot for the "best", even if there's no evidence or reason to believe the "best" is really of great value. I've seen this in my own behavior and that of my spouse (what if the most expensive preschool actually is the best one?)
Also, the aforementioned difficulty of measuring CEO performance perversely becomes an asset. When people don't know the quality of what they're buying, but they feel that quality is very important, they'll turn to any proxy (Harvard on resume, butt was in chair while previous company was doing well) and pay top dollar for that. You can't pay for quality, but it's extremely easy to pay for scarcity if you really want to.
It just comes back to... if you have a lot of money to spend, and the purchase might matter, you'll often be willing to spend a lot for the "best", even if there's no evidence or reason to believe the "best" is really of great value. I've seen this in my own behavior and that of my spouse (what if the most expensive preschool actually is the best one?)