"For an LLM, it is exactly the opposite".
Is it really? LLMs don't have words inside, for the most part they operate by applying transformations to a vector that does not contain any words at all. Words that come out of an LLM are just what sampler gives us by looking at the vector that is the result of those transformations.
Does this vector contain a world model? Some form of thoughts or reasoning to arrive at the result? That's an open question really.
Sure, rerunning that whole process for each token might not be the best solution, although that's an open question too. But saying that LLMs operate on words first is too big of an oversimplification