> the machine that works by generating the most statistically likely text

You've just described a “base models” (or pre-trained model), but later training stages (RLHF, GRPO, whatever secret sauce model makers use) induce a strong bias in the output.

Also, being “statistically identical to human generated text” doesn't mean it's unrecognizable, because human generated text exhibit many various clusters (you're not texting your friends with the same language you're writing a book with) and an LLM can, and in practice, do, use language that is not appropriate for the tone a human expects in a certain context (like when bots write LinkedIn-worthy posts in reddit comment section). The “average human-looking text” is as unnatural to us as a “synthetic average human” with one testicle and half a vagina would be.