Unlike inconvenient lower-level jobs, no one tells the Chief Executive how they are doing. Do managers let their know they are undermining their authority, making poor decisions or communicating poorly? Not likely. Even when a CEO asks for honest feedback, the fear is there. Non-flattering feedback may stall a promising career. Even when a company uses 360 degree feedback, no one penalizes the CEO if they do not act on the feedback.
The board of directors supposedly oversees the CEO but they are far removed from day to day actions. Over time, they can evaluate performance but they look mainly at share price and company strategy. They are rarely interested in the CEO's daily behavior.
By measuring their performance based on their duties, a CEO can learn to do their job better. The CEO's job is setting strategy and vision, building culture, leading the senior team and allocating capital. The last of these is easy to measure. The first three are more of a challenge.