The pirate moves one tab to the left.
When a takedown agency files a DMCA notice with Google and nothing else, the leak page does not lose its audience — it just loses one search entry point. The buyer looking for a free copy of your course, your software, your brand's product photography, or your subscription content simply opens a different search bar. They try Bing. They try DuckDuckGo. They try Yandex. Each of those engines still lists the pirated page, still ranks it, still routes the click. The leak page keeps earning impressions from the engines Google's DMCA database doesn't touch. The pirate doesn't have to do anything. The user moves themselves.