> Can LLMs reliably (that is, with high accuracy and high precision) read, say, literary style from a corpus and output tidy data?

I think they have the capability to do it, yes. Maybe it's not the best tool you can use- too expensive, or too flexible to focus with high accuracy on that single task- but yes you can definitely use LLMs to understand literary style and extract data from it. Depending on the complexity of the text I'm sure they can do jobs that BERT can't.

> they still can't fit anywhere in production

Not sure what do you mean for "production" but there's an enormous amount of people using them for work.