Now, under growing pressure from governments and counterterrorism advocates, YouTube has drastically reduced its video archive of Mr. Awlaki, an American cleric who remains the leading English-language jihadist recruiter on the internet six years after he was killed by a United States drone strike. “It’s a watershed moment on the question of whether we’re going to allow the unchecked proliferation of cyberjihad,” said Mark D. Wallace, the chief executive of the Counter Extremism Project, a research organization that has long called for Mr. Awlaki’s recordings to be removed from the web. “You just don’t want to make it easy for people to listen to a guy who wants to harm us.”