And then what, we're done? How have we avoided the need for the same exhaustive human review? It only saves human review time if you trust the LLM not to miss things.
An LLM could replace the random sampling. It doesn't need to be particularly good for the approach to provide value. I would worry about LLM bias though.
Another thing to consider is that readers can detect fake citations after publication, report to arXiv, and the author gets banned.