We don't train current LLMs to mimic the average human's writing style. We train it to be smart, helpful, and knowledgable, too knowledgeable for a human. We can easily train a LLM to pass the Turing test if we wanted to, but then it would just sound dumb or biased.
> but it would just sound dumb or biased
We have one of those: Grok.
There is tons of money trying to get customer support bots to sound human but they fool nobody.
> We can easily train a LLM to pass the Turing test if we wanted to, but then it would just sound dumb or biased.
Interesting idea. "This is not dumb and biased enough, probably not a human".