Cease and desist letters often come with invoices for use of the work up to that point.
The function of copyright is to allow the creators of a work to reap the fruits of their labor. So, the idea that copyright generates income is not perverted, it’s actually the function of protecting one’s copyright.
The only person(s) who would find this a perversion of copyright is the copyright infringer and those who feel they don’t have to pay to use another person’s work.
Of course there are firms who help copyright owners find infringements and get paid for the infraction. And the firm gets their cut for doing the legwork. How can this be extortion when they are working towards protecting the rights of the copyright owner?
With your logic, I guess when someone gets a speeding ticket, it’s extortion to pay a fine.