Here is the moment this technique is for. The output came back and it is fine. Structurally sound, readable, nothing embarrassing. It is also not the thing you would send to the person who matters, and you cannot immediately say why.
So you start editing by hand. An hour later you have tightened three paragraphs and you still have not noticed that the document never addresses the one objection your reader is guaranteed to raise.
There is a loop that catches that, and you already know it, because it is how serious writing has always been made: write, criticise, rewrite. The only thing missing is that nobody thought to run it inside the conversation.
Do not ask the model to improve its output. Ask it to criticise its output against named criteria, then rewrite from that critique.
Those are genuinely different requests. "Improve this" gives the model no target, so it does the only thing available and rephrases. "Check whether every error state has a defined response body" gives it something it can actually go and look for, and either it is there or it is not.
Why it produces real gains
The published work on self-refinement and reflexion-style techniques keeps landing on the same result: routing output through a structured critique pass measurably improves it, with no extra examples, no fine-tuning and no second model. Evaluating a finished draft is an easier job than producing one, because the draft is now sitting in the context as something to inspect rather than something to invent.
It matters most where the first pass has too many dimensions to get right at once. A specification has to be complete, unambiguous, implementable and secure. A cover letter has to open well, prove impact, avoid repetition and close memorably. First drafts land some of those. Almost never all of them.