We will always need a charismatic human being to be the figurehead of an organization, so I don’t think AI will ever replace CEOs. They will wind up making the important decisions though.
For most purposes maybe it's enough to project charisma in a video.
An AI CEO might also be capable of superhuman "interpersonal" feats like "personally" answering every letter, phone call or complaint.
This terminology is becoming widely used by prominent AI researchers at e.g. Deepmind (Botvinick et al), Stanford (Finn et al), MIT, Northeastern, Meta, etc. as we have to switch to a new goal in lieu of the new advancements that have been coming up in that past few years. Importantly, this shift has been happening behind the scenes independent of this 'OpenAI' craze, although it's obviously made a select portion of the advancements made accessible by the public. There is much more going on than just the GPT series that few people are engaging with, but much is hidden in the literature.
To your point - it's of course extremely strange to conceive of - but while the quirks of human forms may be a useful tool at the moment, there isn't anything necessarily fundamental that requires it for long term.
So, if an AI CEO can execute better than human CEOs, it will dominate.