Rather than some fundamental law of AI, one might better view the Turing Test as a then-obvious product of its social backstory and circumstances. Turing was a son and grandson of civil servants, engineers, army officers, and gentry. He grew up in the inter-war (WWI-WWII) British Empire. He originally called his test "the imitation game". And introduced it in a paper he published in a philosophy journal.

In that context - being able to present yourself as an intelligent human, in strictly written communication with other humans, is a "d'oh, table stakes" human skill. The Empire was based on ink-on-paper communications. If you couldn't keep the people who read your correspondence, paperwork, and reports convinced that you were an intelligent (and dutiful, honorable, etc.) person - yeah.

(Yes, that was only the ideal, and the British Empire frequently fell rather short. But what is an "imitation game", described in a philosophy journal? An ideal.)