It would be almost impossible to prove causation. It's like when they peg the government of the day as 'responsible' for good or bad inflation figures.
There can be large macro decisions made which clearly impact (eg. COVID handouts) but measuring the degree to which they contribute, what the alternative path would have led to, etc, is impossible.
And the myriad of smaller decisions made? Or the clarity with which lower level employees interpret these, and to the extent to which an organisation is mature enough to effectively implement decisions made? No chance.
So they tie CEO performance to measureable items (profit, share price, growth into new markets), make a large portion of their wage up based on 'performance bonuses' and then we all wonder why CEOs take dubious actions which inflate share prices.
*shrugs*
My point was that there isn't that much actual thought or consideration which leads to huge disparities between executive pay and the pay of lower level employees. The standard line we hear is that "executives work so hard" and have so much more "brainpower" than everyone else, and it's ostensibly based on this (and only this) perception which is supposed to explain why some people live in mansions while others have to eat out of garbage cans.
I submit that this perception is not real; it is an illusion with no basis in fact whatsoever. And, as you admit here, none of it can be proven anyway.
Such a perception doesn't even seem to follow the basic economic principles of supply and demand or the iron law of wages.
As an example, sports team owners and Hollywood producers might have to pay a primadonna athlete or actor a high salary because of their rare and gifted talents which lead to popularity at the box office, which translates into tangible profits. Even to get to play on a college team isn't that easy, as one has to have the skills and abilities to compete. So, it would be far easier to prove that a high-paid athlete is worth his/her salt, since they go through tryouts and compete - and there's very little subjectivity or whimsy when it comes to determining who is better.
In contrast, there are probably millions of business administration majors out there - people with the training and vocational skills to manage a business. In labor market terms, they're a dime a dozen. I seriously doubt there's any "labor shortage" at the executive level. The labor shortages seem to be occurring at the lower levels, so if these companies follow basic economic principles, they would be lowering their executive pay and raising the pay of the frontline employees.