This is a non sequitur.
Even if the premise were meaningful (they're trained on human-written text), humans themselves aren't "trained on human-written texts", so the two things aren't comparable. If they aren't comparable, I'm not sure why the fact that they are trained on "human-written texts" is a limiting factor. Perhaps because they are trained on those instead of what human babies are trained on, that might make them more intelligent, not less. Humans end up the lesser intelligence because they are trained less perfectly on "human-written texts".
Besides which, no one with any sense is expecting that even the most advanced LLM possible becomes an AGI by itself, but only when coupled with some other mechanism that is either at this point uninvented or invented-but-currently-overlooked. In such a scenario, the LLM's most likely utility is in communicating with humans (to manipulate, if we're talking about a malevolent one).