You mean, the CEO is only pretending to make the decisions, while secretly passing every decision through their LLM?

If so, the danger there would be... Companies plodding along similarly? Everyone knows CEOs are the least capable people in business, which is why they have the most underlings to do the actual work. Having an LLM there to decide for the CEO might mean the CEO causes less damage by ensuring consistent mediocrity at all times, in a smooth fashion, rather than mostly mediocre but with unpredictable fluctuations either way.

All hail our LLM CEOs, ensuring mediocrity.

Or you might mean that an LLM could have illicitly gained control of a corporation, pulling the strings without anyone's knowledge, acting on its own accord. If you find the idea of inscrutable yes-men with an endless capacity to spout drivel running the world unpalatable, I've good news and bad news for you.