Hmm. I think I understand where you are going but given that LLMs appear to need injected randomness to work effectively, determinism isn't really on the table so we kind of stop talking about the LLMs we use when we (strictly speaking) consider the case where they could generate deterministic sequences?
Not that this in any way takes away anything from your argument that "it's that language is imprecise". That still holds true, but it is on the input side.