Napster only operated as a P2P file sharing service for two years (mid 1999 - mid 2001) but in large it gave birth to the DPI/traffic management industry.
While Napster's founders were sued by the record industry just few months after the service launch, broadband ISPs immediately started to see the impact of music (and later, video) on their peering links, Opex and the whole business model - mainly the smaller ones, or those paying high fees for their uplink connections. Other services that followed Napster - (e.g. Kazaa, Gnutella, Emule and BitTorrent) made the challenge of managing traffic even bigger - due to the increased popularity, higher access speeds and complexity of identifying these applications.
For years, DPI vendors sales to ISPs were almost entirely based on the pain caused by P2P file sharing, and the great ROI achieved by add a "layer 7 traffic management " (later to be called DPI) device to control the traffic they generate.
Recently, the current Napster music service subscribers were acquired by Rhapsody and the service was merged with Rhapsody on-demand music service. Life is short in the internet age.