Interestingly, this is a question my father would ask patients as a paramedic who was trying to assess people's consciousness. Another would be, "what day of the week is it?".
I'd say that these technologies are just like magic - they can seem to do things that defy your expectations, but oftentimes they fall apart when looked at from a different angle.
They would be expected to answer with something matching the day/time distribution that was represented in the training data they used; like the answer to various prompts of the "current president" question is dominated by Trump, Obama and a bit of Bush and Clinton, simply because those are the presidents in the training data and the more recent events simply aren't there yet - like the many models who have no idea how to interpret the word 'Covid' simply because they have been trained on pre-2020 data even if the model was built and released later.
Just a total AI meltdown from one simple question.
https://www.youtube.com/watch?v=CIoBSYpgYRw
For me, I call these Eliza-isms, since it reminds me of its simple formulas like "Can you tell me more about ___" that people got so much mileage out of.