...and they are often run by the same people. They use shell companies to basically avoid take-down requests.

Their goals is to make it sufficiently annoying to take down your information, that most people give up. While at the same time removing it (regardless of the process) for anyone that occupies them too much time - because your individual data isn't valuable enough to waste defending against a take-down.

I suspect a (faux) lawyers letter is easier to get these takedowns processed than the calls/emails that most people try.