That’s one way AI-generated image leaves artifacts and clues. It could even be traces that cannot be seen by human eyes. There will be other signals and it will probably be arms race where forensics will improve, but AI will get even better, so on and so forth. Time will tell.
In terms of data privacy it would become a nightmare.
However I think Zuck would be a massive improvement over spez in terms of strategy, diplomacy, PR rizz and general chill. And this is not a very high bar.