I think it's the height of naivete to believe that music piracy would have ended if only the music labels had struck a deal with the original Napster. I'm not sure why it's so difficult for some people (cough, Boing Boing, cough) to believe that millions of people want music for free--because they're cheap, because they're dishonest, because they simply don't believe that they should have to pay for music.
Had such a deal been struck, it would be no different than it is today with numerous paid music sites. Other pirate services would have sprouted up, and the situation would have been no different. Did the labels lose some money by not getting paid for downloads earlier? Maybe. But they've lost billions through piracy, and that wouldn't have changed.