Indeed. This is easiest to see when you try to translate a poem. Suddenly you become aware of how things like rhythm and metaphor are not confined to poetry, but in fact infuse so much of spoken and written language.
As currently designed, LLMs may eventually come to internalize these values (I do not say "appreciate" them, because I don't think LLMs have any reflective attitude towards what they create). But so much of communication is non-linguistic, and our innate bias is still to credit a person's gestures over their words. I don't see machines getting that anytime soon, so their understanding of language will remain superficial.