Who controls the prompt? Shareholders? And how do you have confidence that the prompt is being used? Just thinking out loud, it’s an interesting idea (even if it might be terrible and dystopian).
Based on existing corporate hierarchy it would probably be the board of directors. There would be some sort of collaboration service where managers/agents push up problems and solutions to the board and they vote yes or no
The grandparent comment of yours mentioned Delamain from Cyberpunk 2077. In that fictional scenario, the company purchased an AI which gradually took over its workforce: maintenance robots, drivers, etc. All that was left was the owners/board of directors, essentially.
What ended up happening was that the AI ended up tricking the board of directors by buying back the company for itself.
You find this out by poking around the abandoned offices of the company and read the emails on the computers. The whole reason you interact with Delamain is that it is basically using your human help to do some tasks that it can't do as an AI (fairly compensated, Delamain actually seems like a pretty stand up AI, and the strange legal status of the company is ignored by authorities because so many people depend on the service).
That scenario is starting to seem highly plausible as long as someone is sets up something badly enough.