This argument comes up often but can be easily dismissed. Make up a language and explain it to the LLM like you would to a person. Tell it to only use that language now to communicate. Even earlier AI was really good at this. You will probably move the goal posts and say that this is just pattern recognition, but it still fits nicely within your request for something that no one ever came up with.
Ask ChatGPT about ConLang. It knows. Inventing languages was solved a hundred years ago with Esperanto.
> but it still fits nicely within your request for something that no one ever came up with
YOU came up with it dawg
I haven't tried in a while but at least previously you could completely flummox Gemini by asking it to come up with some plausible English words with no real known meaning; it just kept giving me rare and funny-sounding actual words and then eventually told me the task is impossible.