But language processing is just one subset of human cognition. There are other layers of human experience like sense-perception, emotion, instinct, etc. – maybe these things could be modeled by additional parameters, maybe not. Additionally, there is consciousness itself, which we still have a poor understanding of (but it's clearly different from intelligence).
So anyway, I think that it's reasonable to say that LLMs implement one sub-set of human cognition (the part that has to do with how we think in language), but there are many additional "layers" to human experience that they don't currently account for.
Maybe you could say that LLMs are a "model distillation" of human intelligence, at 1-2 orders of magnitude less complexity. Like a smaller model distilled from a larger one, they are good at a lot of things but less able to cover edge cases and accuracy/quality of thinking will suffer the more distilled you go.
We tend to equate "thinking" with intelligence/language/reason thanks to 2500 years of Western philosophy, and I believe that's where a lot of confusion originates in discussions of AI/AGI/etc.
[1]: https://medicine.yale.edu/lab/colon-ramos/overview/#:~:text=...