Let's say you are correct.
You ask an LLM to write something for you, and to you it looks really, really good. So based on your conjecture, that means I am not a very good writer.
Ok, but how does that change what I should do? If I am not a very good writer, that means an LLM IS actually better than me, even if it might not be objectively good to an expert writer.
My two choices are to keep producing my own crappy writing, or use an LLM to create better (but not great) writing.
Wouldn't it make sense to use an LLM?
It seems to me your premise leads you to the same conclusion you would reach even if your premise was false; if me thinking an LLM is good at a task means I am very bad at that task, I am probably better off having an LLM do it. On the other hand, if you are wrong, and I think an LLM is good at something because it actually IS good at that thing, then I should also use the LLM to do the task.
Either way, the LLM is better than me at the thing.