How would that change anything? The proposed watermark is applied while the output tokens are being chosen, taking that text and running it through an LLM again would just repeat the process.

It says it only applies to passages over 200 words, so you could use a different LLM to rephrase every other paragraph and undermine the watermarking.

You take the output and run it through another LLM with "please re-write this in xxx style". Then you repeat that a few times on different part of text and glue it all together at the end.