When Anonymous protested, it did two things. First, it sent Miscavige's already significant paranoia sky-high, and it did it in a way that he simply couldn't respond. Even though the cult had the money to hire PI's to follow every single protester, there simply aren't enough PI's in America or elsewhere in the world to hire to follow and harass everyone. The old playbook, which was built with an assumption of a small and manageable number of enemies, simply broke. In other words, the "admin tech" couldn't scale to meet the current threat environment. And the poor saps in the lower levels of staff cheerfully booted the problem up to Miscavige, who saw the cult as being completely under attack by protesters who didn't follow the old playbook. The nerve! They sang songs! They delivered caek!!
While it's likely that Miscavige previously spent a huge amount of time personally directing campaigns against the relatively few public critics of the cult, the increase in number of protesters, plus trying to monitor the online community that the Anons built, probably consumed most of his time and most of his attention for a number of years. And this happened at a critical time, when he was increasingly desperate for new "product" strategies to extract more money from members. In other words, I'm saying that the presence of the Anons slowed and affected the cult's ability to launch The Basics, Golden Age of Dreck Phase II, the Super Power building, and everything else Miscavige needed to keep members loyal. And I strongly suspect that his lack of mental bandwidth caused Miscavige to lose track completely of any attempt to recruit new members.
Second, it cost Scientology its future membership growth. While member growth had already been lagging, word of the Anon protests spread via social media, and the brand because the target not of fear and worry but of laughter and derision. The Anons meant that the majority of people in prime recruiting demographics (in college, young, etc) now knew of the cult and associated it with ridicule and contempt. Thus, an entire generation was lost to body routers and reg's forever.
The Internet itself didn't bring Scientology down. The OT materials were posted in the late 1980s and early 1990s to the alt.religion.scientology Usenet group. Usenet was the Internet in the 1980s and early 1990s. It predated the Web and was a fraction of its size, and the release of the OT "scriptures" was damaging but since only a couple hundred thousand people used Usenet globally, they were only found by people looking for them. There were only a few committed critics, and the OSA internet presence could easily keep up.
Moving OT documents to the Internet didn't inherently cause the collapse of the cult. What was needed to turn the Internet into a weapon was a large crew of people who were able to build a community to push information critical of the cult to the top of search rankings. The Anons did that, through explicit gaming of search engine optimization, but also by building a community with enough links to discussions, documents, etc. that information critical of Scientology was widespread enough that even the simplest Scientology search would turn up with numerous critical articles on the first page of results. No longer could the cult work to outshine critics and push negative information off the front page of a Google search.
I'm thankful that those legions of thousands of protesters did what they did. I'm grateful to those who stayed, who endured the harassment that the cult was able to rain down on selected protesters. The work you all did really has made a difference.