Anecdote: I've had at two friends publish "papers" just by slapping their names on something they had literally nothing to do with, out of pure nepotism.

This wouldn't be helped by an AI watermark. What would help is if the reviewer used AI to look up the authors and see the authorship claims are dubious. The papers are still up.

I do think the academic publishing field is corrupt, which is why I'm not convinced it should be on AI providers to help bail it out of doing its one job (verification and trust).