Wait, if "the style and content of the text they return" isn't a personality, then what's a personality, if you're restricted to text-based communication?
Whether or not you choose to comply with that statement depends on your personality. The personality is the thing in the human that decides what to write. The style and content of the text is orthogonal.
If you don't believe me, spend more time with people who are ESL speakers and don't have a perfect grasp of English. Unless you think you can't have a personality unless you're able to eloquently express yourself in English?
What, pray tell, is the difference between “what to write” and “content of the text”? To me that’s the same thing.
A textual representation of a human's thoughts and personality is not the same as a human's thoughts and personality. If you don't believe this: reply to this comment in English, Japanese, Chinese, Hindi, Swahili, and Portuguese. Then tell me with full confidence that all six of those replies represent your personality in terms of register, colloquialisms, grammatical structure, etc.
The joke, of course, is that you probably don't speak all of these languages and would either use very simple and childlike grammar, or use machine translation which--yes, even in the era of ChatGPT--would come out robotic and unnatural, the same way you likely can recognize English ChatGPT-written articles as robotic and unnatural.
[0] https://en.wikipedia.org/wiki/Map%E2%80%93territory_relation
Moreover, if "personality is the thing ... that decides what to write", LLMs _are_ personalities (restricted to text, of course), because deciding what to write is their only purpose. Again, this seems to imply that LLMs actually have personalities.
An LLM does not have a favorite movie until you ask it. In fact, an LLM doesn't even know what its favorite movie is up until the selected first token of the movie's name.