From my perspective, the disconnect you describe is one of the main reasons this term cannot be applied.
Another reason is that the argument for calling LLMs conscious arises from the perspective of thinking and reasoning grounded in language.
But in my personal experience, thinking in language is just a small emerging quality of human consciousness. It is just that the intellectuals making these arguments happen to be fully identified with the “I think therefore I am” aspect of it and not the vastness of the rest.