What about if we are converging instead on Asimov's robots? I would imagine "like a human" wouldn't at all be what we are working towards but instead a superhuman which the robots of his short stories often were.

The two issues with that is (1) they did effectively let humanity "look at the source" in that a big part of the stories was the corporation attempting to get humans to trust the robots by implementing the three laws in such a way that it would be impossible to circumvent (and making those laws very widely known). Didn't work, humans still didn't trust them. (2) as far as I know the operators of LLMs don't seem to currently have a way to give instructions that can't be circumvented quite easily.

Viewing the source and having that source be ironclad was, for Asimov at least, a prerequisite to even attempting to integrate superhuman technology into society.