Companies like Verizon don't casually threaten legal action, this is really getting to them.
(Perhaps because one of Verizon's unique selling propositions is the quality of their networks, this has the potential for broad damage to their brand.)
Why would you say this is a "demonstrably successful" action, btw? Has Verizon actually changed any of their business practices for the better? So far, all I can see is that they are tossing around legal threats. That's not progress; that's Verizon's gigantic legal team gearing up to make sure Verizon can continue to do Absolutely Nothing Positive about the issues in question.
Right now I don't read that threat as credible, but, let's say, how about after the first few Congresscritters are sent home to spend more time with their families after an election? We gun owners, probably less numerous than voting Internet users (don't believe gun ownership self-reporting in surveys, for obvious reasons), with nothing more than our organized votes, have moved mountains at every level of government over the last three decades. Ask ex-Speaker of the House Tom Foley about our power (first Speaker to be turned out of office since the Civil War in 1862).
As the Internet, and good Internet service, gets every more important, the potential is there. Getting back to my analogy, the gun grabbers had a fantastic run for a couple of decades (or more than a century, depending on how you count this and gun control starting to really bite non-minorities), before politically effective resistance started showing results.
Are you sure? As someone who has dealt with more than 40 different threats of legal action from major companies, I would have guessed that this is more or less their default response.
It also depends on the domain, e.g. Disney protecting IP or ASCAP uncompensated public performances is one thing, and the latter's model can run into PR buzz saws, e.g. Boy and Girl Scouts sings at camps.
Whereas this is part of a big fight that goes right to the heart of a significant part of Verizon's business, and an even more significant part of their potential future business. When Disney threatens a day care center for having an unlicensed depiction of one of their characters, it's routine. Whereas I expect this threatening letter to Netflix was run way up the flagpole; Verizon hasn't typically been that maladroit with PR, have they?
In what domains have you received threats of legal action?