Nothing like a little anthropomorphism to completely distort otherwise good faith interpretations of bot behavior.
You of course know that the model is not capable of thought or reasoning - only the appearance of them as needed to match its training corpus. A training corpus of completely human generated data. As such, how could anything it does, be anything but anthropomorphic?
Now, if this model were trained exclusively on a corpus of mathematical proofs stripped of natural language commentary, the expectation that you seem to have would be more appropriate.
Do we know? It's the reverse Chinese room problem. :p
I aspire one day to find the free weekends and adequate hubris to build a benchtop implementation of Julian Jayne's Bicameral Mind with 1+N GPT-3 or GPT-neo instances prompting each other iteratively to see where the train of semantics wanders. (as I'm sure others have already)