While I am intimately familiar with the Swiss Cheese and Links in a Chain theories and other aspects of aviation safety, I recognize the limits of the most well-intentioned corporate culture and the ability of even the most proficient senior executives in preventing accidents. I agree a culture (of safety) permeates throughout an organization, though not necessarily from top-down. Indeed, it's quite often the middle management and line supervision that have more direct impacts on enhancing/reducing the chance of adverse occurrence. Bad things happen to good airlines. Conversely, we also have airlines with abysmal regard to safety somehow managing to muddle through without frequent and serious incidents, likely thanks due to aircraft design, parts/procedural redundancy, regulatory oversight, individual skill and blind luck.
My point remains that notion of "the lives of millions are in his hands" is problematic, and senior executives should not be compensated as if they could prevent tragedy.