Executives are supposed to work for the shareholders.

If the executives of Uber could just ignore shareholders, they wouldn't need to worry about profits at all.

They do work for shareholders but since shareholders aren't equally divided, i.e. one person or company may own a larger portion, and it's difficult to sue over this, executive can ignore the shareholders to an extent.

How would you prove a decision was wrong without hindseight? How would you prove an executive shouldn't make X amount of money?

Imagine I'm the CEO of Nike, I make $100 million a year. The company is doing amazing. Is that because of decisions I made, marketing, good product, word of mouth, things that happened before I was CEO. Prove that I shouldn't get that money.

There's no need to prove anything: the shareholders can replace the CEO (via some indirection) at will.

They don't get the money back they already spent, of course.