The CEO does not set his own compensation. He is hired by the owners of whatever company to operate it for them. They ultimately determine the compensation.
I agree there’s no struggle to find top candidates, that’s for sure. That’s partly because the compensation tends to be very good. The trades, which do not compensate as well as a chief executive, are struggling more. If plumbers frequently pulled CEO pay, we would not have a shortage.
I never said it was fair, don’t get me wrong. How it got this way vs whether that’s a good idea or not are two totally separate topics.
I’m not sure that most boards of directors are full of CEOs either. It is full of rich people though.