The issue isn't that good CEOs add a lot of value - clearly true. The issue is why are they being allowed to capture that value despite fierce competition? Nobody else is allowed to do that. If there are 10 willing & hypercompetent people paid <$1,000,000 available to do your job, it shouldn't be feasible for you to earn >$2,000,000 unless there is something very strange happening. Like a very effective guild system and control of the corporate budget.
Exactly as you say, it isn't like we can differentiate between these people in advance. Why do we think paying them more will help? In any other field you can get exceptional talent for far less than a CEOs salary.
Of course. And to be clear I'm not quibbling about CEO pay being higher than the minimum wage.
The question that I've an issue with is how much larger. Back in the 1950s the answer seemed to be 20x the minimum wage or whereabouts. Nowadays it's more like 360x. [0]
CEOs were doing the same kind of job at the time.
And just think about it: it means the typical large company CEO earns in one day what his baseline employees earn in a whole year. That's just a recipe for a French or Russia style Revolution to erupt.
Plus, who actually needs $1M/year? I've earned fairly good money for years -- but still a fraction of that -- and I'd have no idea how to spend that much without investing up the wazoo. And in case you're thinking "I'd know how", sure, the answer is yes, everyone does -- for a few months. As a salary, $1M/year is ludicrous. And $10+M/year is sociopathic. No one is worth that much.
[0]: https://www.forbes.com/sites/dianahembree/2018/05/22/ceo-pay...
Of course why you would pay such high salaries to a CEO who is untried and might turn out to destroy the company is a valid question.