To my mind the CEO job at scale is 4 things - Keeping the fight fair-- The leadership and executive management should argue viciously, The CEO should make sure these conflicts remain constructive and aligned with company goals
Holding the vision true-- There's a risk of mission drift, continually reinforce and refine the company's vision, make sure all leaders remain aligned with longterm goals
Enforcing strategic adherence-- A strategy is only as good as its execution. ensure the leadership team not only understands the strategy but implements it across all levels of the organization. Manager of Leaders
Deal with the real world-- Q-calls, investor relations, supply chains/vendors/etc.
This is often the problem I have with business advice, it's general but not generally applicable. Scale matters probably most in the context, followed by the type of business.