I'm afraid watermarking could restrict applications where LLMs can be safely used to assist with writing. If I write something myself and use an LLM to proofread it, without watermarking I can confidently say that corrections done by LLMs are small and insignificant enough to claim that the text is still authored by me, not by the model. With watermarking, however, I will never be sure if the result will not be flagged as AI generated, even if the AI contribution is very minor.

Watermarking will not flag something you wrote unless the AI rewrote significant chunks of it. AI watermarking works by exploiting the fact that lengthy phrases can be expressed in exponentially many ways, such that the selection of a single sequence from the exponential space is practically unique. For proofreading by contrast, if the AI is only changing isolated words in work that's otherwise yours, there are not enough exponentially branching options for the watermark to distinguish anything.

*Some might see a parallel with the old game Adventure, in which wording differences like "twisty little passages" and "little twisty passages" were used to build a maze of room descriptions, with the same meaning but still distinguishable to the attentive player.

I think if you use an LLM just to proofread then it'll not be able to insert a strong enough watermark.