The argument is that the best writing is the unexpected, while an LLM's function is to deliver the expected next token.
The first requires intention, something that as far as we know, LLMs simply cannot truly have or express. The second is something that can be approximated. Perhaps very well, but a mass of people using the same models with the same approximationa still lead to loss of distinction.
Perhaps LLMs that were fully individually trained could sufficiently replicate a person's quirks (I dunno), but that's hardly a scalable process.