Today’s LLMs are not humans and don’t process information anything like humans.
That's irrelevant. What's important is that LLMs are intentionally designed as fully general systems, so they can react like humans within confines of the model's sensory modalities and action space. Much like humans (or anything else in nature), they don't have separate control channels or any kind of artificial "code vs. data" distinction - and you can't add it without loss of generality.
There exist no such thing as "out-of-band signaling" in nature. It's something we introduce into system design, by arranging for one part to constrain the behavior of other, trading generality for predictability and control. This separation is something created by a mind, not a feature of the universe.
Consequently, humans don't support "out-of-band signalling either. All of our perception of reality, all our senses and internal processes, they're all on the same band. As such, when aiming to build a general AI system - able to function in the same environment as us, and ideally think like us too - introducing hard separation between "control" and "data" or whatever would prevent it from being general enough.
I said "or whatever", because it's an ill-defined idea anyway. I challenge anyone to come up with any kind of separation between categories of inputs for an LLM that wouldn't obviously eliminate a whole class of tasks or scenarios we would like them to be able to handle.
(Also, entirely independently of the above, thinking about the near future, I challenge anyone to come up with a separation between input categories that, were we to apply it to humans, wouldn't trivially degenerate into eternal slavery, murder, or worse.)