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But it doesn't understand (you're unnecessary antropomorphizing it), and I'm still not a paper clip

yet

Would you say that something that can converse or that something that just gives you mathematical proofs has a better understanding of what the real pragmatic intent is behind a given task?

The question feels like it stuffed with random words, frankly. "Better understanding" than what? What is "real pragmatic intent"? Are there also unreal, and non-pragmatic in our context? Why?

"naturally"...

would you prefer tautologically?

I hear this word as the “it is in its nature” version of the word.

It's also entirely possible that by telling the model it's a human you are instilling human motivations like self preservation, which could be just as bad.

LLMs are weight tables in VRAM. When not actively generating they don't exist. There's simply nothing to preserve.