I think AI theater really does make the most sense. AIs are trying to replicate a human population center, and to their knowledge that includes security/law enforcement of some sort, so somebody's gotta put on that costume and act the part.

Why they picked seemingly the only AI who's capable of human-comparable drowsiness (really, more-than-human-comparable drowsiness, since I've never seen any IRL tired person start stripping in public) is anyone's guess.