The domain expertise I'm referring to isn't vague, it literally doesn't exist as training data. There are no cases of problems and solutions to study that are relevant to the state-of-the-art. In some cases this is by intent and design (e.g. trade secrets, national security, etc) long before for LLMs arrived on the scene.

We even have some infamous "dark" domains in computer science where it is nearly impossible for a human to get to the frontier because the research that underpins much of the state-of-the-art hasn't existed as public literature for decades. If you want to learn it, you either have to know a domain expert willing to help you or reinvent it from first principles.