The RIAA filed a lawsuit against Napster in December 1999. A preliminary injunction to block RIAA music on Napster was granted in August, 2000. Napster appealed and the circuit court upheld the injunction in February 2001. The injunction was effective as of March 2001 and Napster shut down in July 2001. Some of the lawsuit was settled out of court in September 2001. Napster went bankrupt in September 2002.

So that's 15 months for a slam-dunk injunction. Today it wouldn't take as long since there's case law backing them up. But if the RIAA had spent 2 years sending emails and writing blog posts, they wouldn't have gotten anywhere either.