At my current job, a 10 person startup, the CEOs job is to generate leads, talk to potential customers, and close deals. He, along with the other founders, shape what we work on based on what he thinks it’s possible for us to sell. He’s essential to the business.

At my previous 50k person company I never talked to anyone within 4 levels of the CEO and thought he was useless. But realistically he probably had a somewhat similar job - talking with the board, talking with politicians, and talking with the CEOs of other companies in the effort to lower costs (tax breaks, partnerships, etc) and generate sales (contracts, partnerships, etc).