...showing someone can destroy or damage a company does not show they can run one excellently...What it shows is that the marginal effect of a CEO is large - multiple percentage points of the company's value. Therefore, the difference in value between a good and bad CEO is equally large.
Gizi: "If the right guy manages the joint, it will do $11 billion. Are you willing to pay 10 million a year for this person?"
Repeat the math with $10B and $7B, and you'll still see that $20M or $50M is a very reasonable pay package to get the guy who is less likely to screw things up. Of course, if you truly believe CEOs have an insignificant effect, I encourage you to invest in companies with CEOs who are perceived as being terrible.
These results came from data that compared CEO remuneration to average employee remuneration.
Your linked study provides very weak support of these claims. It's restricted to bank holding companies and thrifts during the financial crisis. In fact, there is a pretty obvious alternate explanation of it's results - banks with a high pay ratio consist of a CEO + lots of tellers, mortgage officers, etc (e.g., Citi, Countrywide). In contrast, banks with a lower pay ratio consist of CEO + quants, traders, etc (e.g., Goldman, Morgan Stanley).
Can you think of another reason why banks with lots of mortgage officers might have performed worse during the crisis?