I'm trying to understand why you need the LLM.
Let's say that an LLM is around 500GB. If Alice and Bob both have access to shared 500GB, why does the fact that the 500GB is an LLM give them something special?
For example, in 500GB, we could simply have a vast lookup table that converts innocuous text to secret text.
GM = Meet you at the cafe at 5PM.
It's sunny here = We have been discovered.
....
What am I missing here?
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It's not really comparable. The problem with a code book is it won't generate plausible messages longer than a word or two. Afaik your technique has been in wide use amongst spies for many years, but it's exceptionally bandwidth constrained if you want to remain undetectable, and can't support messages of an unpredictable type.