How is the impression of playfulness not a good faith interpretation?

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.