What CEOs Do

If the CEO is primarily focusing on one of these domains (product, operations, PR) who is the individual responsible for debugging the flawed human systems everywhere else in the company?

In my opinion, every level of leadership is accountable for every action of every individual under them (because they either hired the person, or hired someone who did), and thus the CEO is the only role uniquely qualified to fix everything. However I get the impression most hole themselves up in their office with some charts, talking to the board, and meeting with other C-level people (but rarely going to the front-lines).

It's my experience that an implicit class system is formed (based on resumes) where titles only associate with like titles, even when many of the most brilliant individuals are not even in management at all.