I'm not sure if I could have enough storage to store a local copy of every game, movie, and TV show that I'll need to keep myself entertained for a lifetime. Saving a copy of every YouTube video I ever watched would probably go into dozens of TB on it's own.
It would be pretty cool if there was a free peer to peer storage network to store this kind of stuff. The copyright holders would never go for that sort of thing, though.
Even it it was all copyright free material, you know that some jerk would eventually store kiddie porn or explosive schematics on it and get the system shutdown by the feds quickly.