Another thing is also that email itself was not designed with encryption in mind and because it is decentralized and backwards-compatible it is hard to enforce new rules (everyone should use PGP).
But PGP is useful if both sender and receiver agree to use PGP.
I think you are conflating composition and prediction. LLMs don't compose higher abstractions from the "axioms, symbols and rules", they simply predict the next token, like a really large spinning wheel.