I am actually rather fond of caveman. I haven't evaluated it for token cost, in part because frankly I think that part of the pitch is a load of malarkey. Output that's shown to the user is such a small percentage of overall tokens these days.

But anecdotally I do think it saves me quite a lot of time on reading LLM outputs. And that, if nothing else, is good for my sanity.

The caveman gimmick makes sense to me as a clever hack. Caveman talk is a longstanding meme that's presumably well-represented in the models' training data. So just asking it to do that is just an ultra-concise way to tell the LLM to be ultra-concise. Which, in turn, is theoretically good for accuracy because putting too many instructions in the prompt is bad for task performance.