The better product managers will quickly pick up on the (measurable) user frustration generated that way, and from there it's technically trivial to alter the LLM prompts such that the bot simulates being annoyed in a plausible way when tested like this.
The version that was paradise was rejected for being too perfect.
They had to model a version during a time of strife so people wouldn't question it.
Companies don’t want customer support representatives to show annoyance or frustration even if they’re human; wasting time and resources adding that unhelpful behaviour to chatbots just to deliberately trick the minute number of people who use these techniques is absurd.
And it’s irrelevant because (it should be obvious) neither I nor the OP claimed this was a solution to distinguish humans from bots forever. It was just a funny story of something that was effective now in one specific scenario.