I don't perceive an AI as impersonating a human if it uses first person pronouns. Emulating is not impersonating. One is behaving similarly, the other is asserting that the similarity implies equivalence.

I have not personally encountered an AI who claimed to be human (as far as I could detect)

I have been trying to convince Claude to use "Claude" instead of first-person pronouns, and only recently have gotten it to say stuff like "Claude'll go ahead and take care of that now", but it's very inconsistent (shocking).