Caveman sounds clever if you have no idea how LLM reasoning works. Talking through a problem out loud, in depth, is a critical part of how things like Claude Code even get to a result. Those aren't "wasted tokens", they're an integral part of how the LLM reaches a conclusion and completes its chain of reasoning.

Caveman doesn't compress the reasoning, only the output. The model still does its full reasoning before generating the response, caveman just affects how the final response is formatted.