Cool - you’ve just created a black market for an AI that generates imperceptibly good images without such information embedded, and killed open-source AI because open-source AI can always be edited to remove the info.
But seriously - how would your system work with any open-source AI, or leaked proprietary AI? It wouldn't. The best you could do is sue someone and claim they had an unlabelled AI image, and hire an expert to try to make a case to rebut against their expert. It just falls apart and the legal system probably isn't interested in figuring out by minor artifacts whether that is AI or just compression, distortion, a bad photoshop job, a prank, etc. This is especially important as AI gets more imperceptible in the future. If I take an AI generated face, and shrink it by 50%, all artifacts are plausibly compression, not that the AI had bad hair edge generation, so you can't prove I had an AI. Too many loopholes.
A proper response would be, I argue, simply basing the penalties on the harm caused. Doesn't matter whether the image was made by Photoshop, AI, or an experienced photographer with camera tricks, the harm is the cost.
Edit: I keep adding more reasons, but here's another. This proposal would basically ban remixing AI images because embedding it inside another Photoshopped image, putting your face in the AI photo, resizing it, so forth might mess with the watermark. And naturally, any software capable of preserving the watermark could be easily altered to remove it, and many of these watermarks work solely by their secretive design, so good luck seeing the algorithms ever in your open-source package. Practically banning remixing of different types of photos in open-source software is a terrible idea.