Music does take up a lot of storage, especially if you don't compress and use FLAC. But a lot of that is because people haven't paid for their music. Now if I wanted to d/l every episode of Seinfeld to access whenever and wherever I want, then my storage needs increase 10-fold.
Realistically, without pirating music and video the vast majority of people would never spend the money to have enough content to actually fill a 1TB drive (granted, that's only like 150 HD movies, which isn't overly cost prohibitive for movie buffs/collectors).
On the other hand, when LTE does cover the whole US, I likely ditch any sort of online storage options (limited by capacity or price) and just access everything over my home server that I can play easily on-demand. There's still pockets of 3G or no-service around the country, however, which is a problem for some. Not to mention travelers on an airplane still need the foresight to d/l/transfer whatever content they intend to use while on the plane with no signal.
Maybe the HBO GO app will eventually make the leap to letting us d/l a digital copy of content. I can already watch online as many times as I want, so at some point they should figure out how to let me d/l to watch off-line for as long as I remain a subscriber. Plus, with their "watchlist" feature to let me know when new episodes of favorites are available, that d/l could be set-up automatically.