Well, so do most CEOs.
For example an open-source project could/would still have a BDFL but, the AI-CEO could do the operational busywork while the BDFL is out talking to humans and presenting at PGCon or some other productive thing.
This is not a competitive advantage
Most times it's pretty simple, in my experience. A CEO either runs a business as a (1) Sales focus [best deals and vendors] or (2) Marketing focus [best reputation and trends] or (3) Investor focus [best boardroom friends].
Lots of other opinions are usually thrown out until there's really only one facet used for running the company.
So they need someone to review AI output huh?