I think the role of a public regulatory body is necessary. To leave it up to individuals to police their own content or to constantly be on the search for, or vigilant about, their own likeness being used on the web is an unrealistic expectation. For individuals to have to maintain their own protection in that way, I think it underestimates the level of accessibility and widespread use of the technology and how difficult this is.
I know it's also happened to voice actors for video games. They have had their likeness used and manipulated. For people with these fan bases, like you said, if they're not Taylor Swift.... Individuals with a smaller following can be recognized, and it's difficult for them to locate all of the content and constantly notify different hosting platforms to have it removed.
I don't think this idea of self-policing is a practical solution.