Capitalism requires that capital is owned and controlled by specific people. So, no, there cannot be an AI CEO. In other words, if you say you have an AI CEO, then that entity will be under the control of someone else, whom you might as well call the real CEO.
Just like how Twitter had a “CEO” who was some pliable female who did the bidding of the real CEO: Elon Musk.
> Capitalism requires that capital is owned and controlled by specific people.
That is an overly simplistic description. One can imagine a board of directors voting on which AI-CEO-as-a-service vendor to use for the next year. The 'capital' of the company is owned by company, the company is owned by the shareholders. This is not incompatible with capitalism in principle, but wouldn't surprise me if it were incompatible with some forms of incorporation.
The way AI (and capitalism really) makes CEOs obsolete is by replacing all companies with just one. So only one CEO needed eventually.
There are shareholders/owners and CEOs. You can certainly have an AI CEO if the board of directors wants that. Although depending on the jurisdiction CEOs might need be humans, but surely not everywhere.
And you could even imagine AI owners with something like Bitcoin wallets. So far it wouldn't work because of prompt injections but the future could be wild.