I believe that there are two responsibilities a CEO cannot give away or delegate: deciding who works for them, and the strategy / vision / direction of the company. Which is interesting, because I make my living helping companies build and execute strategic priorities.
Really, if I think about it, my role is to create the habit of strategic thinking and execution inside their companies. Not just an event that happens once a year. I consider myself successful when I’ve worked myself out of a job. My clients “graduate” when they exercise disciplined strategic review and energetic execution for themselves.
How do I know when their ready? First, they have priorities. Second, the way they spend all their individual and company resources (time, money, materials, people) lines up with what they say their priorities are. Third, they are successful doing so (for whatever their definition of success is), and can vigorously confront or adjust for any obstacles to that execution.
If you need a little more strategic thinking in your organization / team / company / life, this article talks about the role of the strategist / strategy in a company: