Yes, this is actually a reason why an AI executive could be a formidable alternative in theory.

The CEO is ultimately an employee of the board, and managing the CEO with respect to the board's oversight and interest is a somewhat adversarial challenge.

However, the AI CEO's intentions are fully transparent to the board and entirely pliable to the board's demands. The AI CEO also offers the board the opportunity to retain significant equity shares that materially impact their wealth - in this way AI executives stand to be an even more tantalizing target than fixed labor costs.

Of course, this presumes LLMs will become reliable enough for this, which doesn't seem likely.