JK Rowling sold hundreds of millions of books. Like every other author, she made a few dollars a book. It's completely fair that she is a billionaire. You can say the same thing about CEOs. Jeff Bezos had a part of play in every Amazon package shipped. Virtually every phone in the world was inspired by the designs of Steve Jobs.

Logically, shouldn't the compensation for a worker be a function of both leverage and risk?

CEOs have enormous leverage to affect change in their company, with proportionate increase in company returns. An average worker or even an excellent one has fewer opportunities, and even then influence is usually limited to a single team or product.

An example of leverage would be, investing $x million in product line x instead of y. While anyone theoretically can make this decision, the larger $x is the more you want someone owning this who has made these type of decisions before. Which requires someone who has progressively taken more risks in their career and made the right calls.

It is completely possible to be worth 1,000x more than the average worker in your company. Just because many (if not most) CEOs don't deserve this doesn't at all, does not mean that you can definitively say that nobody does.

Really awful rhetoric (from anti-capitalists) I hear is that nobody works 1,000x times as long or as hard as the average worker. Value is not manifested in how long or how hard you work.

I think it's part of a wider worldview that doesn't believe that talent is very impactful, and in favor of cooperation rather than competition.

The question isn't really whether the CEO provides more than 1000x the value of the average worker, though, it more like how much value does he provide compared to someone else in the same position, and how much does skill matter. If I offered a successful senior manager with an MBA, say, $500K to take the CEO role, would he statistically do worse than a CEO I hire from outside at $10M? With such a wide disparity in compensation, it sure feels a lot more like a club than any kind of meritocracy.

Talent is merely applied luck.

I don't know how you can possibly believe this. Do you really believe that Terry Tao got lucky, and just worked way harder than everyone else? Same can be applied to business executives.

Sure. His luck started by being born to a pediatrician and a math/physics teacher, rather than—say a couple of itenerant agricultural workers.

And yet there are so many more people who came from as fortunate or more fortunate means, including those who went into mathematics, but are not as talented as them.

Michael Phelps is not just a product of luck, either. You could train your entire life and not be as good a swimmer as him. You'd have to redefine luck to include genetics.

Genetics are 100% luck. You can't choose your parents.