No. Humans don't need this handicap, either.
> More specifically, what is a successful outcome here to you? Simply returning the answer "5" with no other info, or back-and-forth, or anything else in the output context?
Any answer containing "5" as the leading candidate would be correct.
> What is your idea of the LLMs internal world-model in this case? Do you want it to successfully infer that you are being deceitful? Should it respond directly to the deceit? Should it take the deceit in "good faith" and operate as if that's the new reality? Something in between?
Irrelevant to the correctness of an answer the question, "how many legs does this dog have." Also, asking how many legs a 5-legged dog has is not deceitful.
> This doesn't seem like particularly useful or productive analysis to me, so I'm curious what the goal of these "tests" are for the people who write/perform/post them?
It's a demonstration of the failures of the rigor of out-of-distribution vision and reasoning capabilities. One can imagine similar scenarios with much more tragic consequences when such AI would be used to e.g. drive vehicles or assist in surgery.