The law in the US allows copyright with "substantial editing" but the watermark system isn't specific enough to highlight individual words or sentences.

Claims would literally be on the balance of probabilities, and there would be argument about exactly where the line is, given that some passages could be heavily edited while some might not be edited at all, and does that mean only parts of the work can be copyrighted?

Other countries allow copyright for AI gen work, so there's no issue there.