If one reads the dialogue, Socrates is not the one "saying" this, but he is telling a story of what King Thamus said to the Egyptian god Theuth, who is the inventor of writing. He is asking the king to give out the writing, but the king is unsure about it.

Its what is known as one of the Socratic "myths," and really just contributes to a web of concepts that leads the dialogue to its ultimate terminus of aporia (being a relatively early Plato dialogue). Socrates, characteristically, doesn't really give his take on writing. In the text, he is just trying to help his friend write a horny love letter/speech!

I can't bring it up right now, but the end of the dialogue has a rather beautiful characterization of writing in the positive, saying that perhaps logos can grow out of writing, like a garden.

I think if pressed Socrates/Plato would say that LLM's are merely doxa machines, incapable of logos. But I am just spitballing.