Cloud Drive is one thing, but I think that Cloud Player has the really interesting, disruptive potential with respect to services like Pandora, Last.fm, and even Youtube and ITunes.
People listen to a lot of music on each of those services. The way I see it, each is just an approximation of the holy grail: the ability to listen to any song, anytime, on demand, for free.
Youtube comes close, but it has quite a lot of music that's only available in low quality and quite a bit that's blocked on copyright grounds.
ITunes fulfills the other requirements, but is not free.
Pandora is free, on-demand, and high-quality, but you have limited control over what you listen to and they have fairly disruptive audio ads.
Cloud player could come closer to goal.
I think Cloud Player could benefit indirectly but massively from the fact that music piracy is common. Many people I know (and, I'd venture, many people on HN) have music libraries in the tens of GB--obviously not obtained by paying $0.99 per song.
How could Amazon offer, say, 100GB for a small enough price (much smaller than the current $100/year for Cloud Drive) ? You mentioned that Dropbox does deduplication.
There's huge overlap between most people's music collections. Quite a few IPods I've seen contain exactly the same 500MB Beatles' discography. It's an awesome use case for deduplication. I think that as long as they restrict uploads to music (and, perhaps, movies), they could pull this off for surprisingly little storage cost on their end.
Combine it with the aggressive CDN strategy they already have (to reduce bandwidth costs), and you could have the the next killer music app. Imagine your own curated, high quality music collection, streamed to you anywhere for a buck or so per month, with the app available for free on all the major platforms.