I don't think AI is going to replace management consultants any time soon. What would the prompt be? You can't possibly explain all the necessary background details to get a useful answer (let alone the actual optimal answer). And even if you tried, allegations of prompt engineering would take you right back to the same political stalemate.

Put another way, if a group of humans could agree on a problem statement and goal, then they wouldn't have a problem anymore.

Perhaps if the AI grew up with the company and was able to ingest every email, chat message, sales data, etc...

Anyway, what's an example of a "scientific fields where everyone within it is required to believe things that are false"? That's quite a claim.