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.
For example, I think "chain of thought" is a good name for what it denotes. It makes the concept easy to understand and discuss, and a non-antropomorphized name would be unnatural and unnecessarily complicate things. This doesn't mean that I support companies insisting that LLMs think just like humans or anything like that.
By the way, I would say actually anti-anthropomorphism has been a bigger problem for understanding LLMs than anthropomorphism itself. The main proponents of anti-anthropomorphism (e.g. Bender and the rest of "stochastic parrot" and related paper authors) came up with a lot of predictions about things that LLMs surely couldn't do (on account of just being predictors of the next word, etc.) which turned out to be spectacularly wrong.
Tbh I also think your comparison that puts "UI events -> Bits -> Transistor Voltages" as analogy to "AI thinks -> token de-/encoding + MatMul" is certainly a stretch, as the part about "Bits -> Transistor Voltages" applies to both hierarchies as the foundational layer.
"chain of thought" could probably be called "progressive on-track-inference" and nobody would roll an eye.