If AI ends up running companies better than people
Okay, important context there. The current AI bubble will burst sooner or later. So, this is hypothetical future AGI.
Yes, if the process of human labour becoming redundant continues uninterrupted, it's highly likely, although since CEOs make their money from the intangible asset of having connections more than the actual work they'll be one of the last to go.
But, it won't continue uninterrupted. We're talking about rapidly transitioning to an entirely different kind of economy, and we should expect it will be similarly destabilising as it was to hunter gatherer societies that suddenly encountered industrial technology.
If humans are still in control, and you still have an entire top 10% of the population with significant equity holdings, there's not going to be much strategy to the initial stages. Front line workers will get laid off catastrophically, basically, and no new work will be forthcoming. The next step will be a political reaction. If some kind of make-work program is what comes out of it, human managers will still find a place in it. If it's basic income, probably not. And if there's not some kind of restriction on the top end of wealth, as well, you're at risk of creating a new ruling elite with an incentive to kill everyone else off, but that's actually a digression from the question.
When it comes to the longer term, I find inspiration in a blog post I read recently. Capital holdings will eventually become meaningless compared to rights to natural factors. If military logic works at all the same way, and there's ever any kind of war, land will once again be supreme among them. There weren't really CEOs in feudalism, and even if we manage not to regress to autocracy there probably won't be a place for them.