The language of "generator that stochastically produces the next word" is just not very useful when you're talking about, e.g., an LLM that is answering complex world modeling questions or generating a creative story. It's at the wrong level of abstraction, just as if you were discussing an UI events API and you were talking about zeros and ones, or voltages in transistors. Technically fine but totally useless to reach any conclusion about the high-level system.
We need a higher abstraction level to talk about higher level phenomena in LLMs as well, and the problem is that we have no idea what happens internally at those higher abstraction levels. So, considering that LLMs somehow imitate humans (at least in terms of output), anthropomorphization is the best abstraction we have, hence people naturally resort to it when discussing what LLMs can do.
Anthropomorphizing might blind us to solutions to existing problems. Perhaps instead of trying to come up with the correct prompt for a LLM, there exists a string of words (not necessary ones that make sense) that will get the LLM to a better position to answer given questions.
When we anthropomorphize we are inherently ignore certain parts of how LLMs work, and imagining parts that don't even exist
exactly. The opposite is also true. You might supply more clarifying information to the LLM, which would help any human answer, but it actually degrades the LLM's output.