Seems to me like this creates a huge incentive to game the watermark. Also, how does it prevent having AI generate the text, then the user copy-paste it into a clean document?
Computerphile on YT has a video explaining how models can fingerprint the text they produce. Essentially they modify the probabilities of word choice slightly in a predictable way.
This would imply that a positive watermark signal is likely (but not guaranteed) to be AI generated. Also implies that a negative watermark signal is not necessarily void of AI generated text. This would create a problem if people start to trust the watermark as a heuristic, as the ability to critically evaluate the text is replaced by the search for a watermark.
Seems to me all of this is really trying to solve for "is this text bullshit" or not, which would require a different solution.