I would say that the difference between your example and these reputation managers is that they are often themselves directly responsible for the problems they create:
Yep, the reason they are so effective is because they own the very website that is spreading the slander. So you're really just indirectly paying the website who's blackmailing you to remove the blackmail.
https://www.nytimes.com/interactive/2021/04/24/technology/on...
I guess this is more analogous to flipping someone’s breakers in their house and then charging them to flip them back on.