For example, take health insurance claim denials (in the US).
Among issuers who reported the highest volume of in-network claims in 2021, receiving over 5 million claims, denial rates ranged from 5.7%. to 41.9% (Source: https://www.kff.org/private-insurance/issue-brief/claims-den...)
In every one of these cases, the insured receives an "Explanation of Benefit" that lists the claims and a "Denial Reason" along with the "Paid, Denied" amounts. On paper, the LLM approach you outlined above looks like it would fit this claims processing workflow. But, it would be another 50 years, if that, before the health insurance industry takes that approach.
Healthcare claims processing is already messed up. Good luck pitching an LLM based system for this.
ps: The simple reason for the resistance/inertia is not technical, but regulatory/legal risk. If the insured sues the insurance company, the company can bring their engineers as witnesses to explain how the denial logic has been coded. There is no way (at least currently) to explain why an LLM model took a certain decision. As long as there is the risk of the LLM hallucinating on the witness stand when prompted by the suing party's lawyers, there is no way the business/risk teams would sign off on that.