Millions of people don't appear to share your concern when it comes to their personal email accounts, which are arguably more valuable than a few documents...

Actually the majority of computer users have no form of backup, despite how easy it should be. Lose your laptop/iPhone/hdd crash, and many people find themselves lost with no backup.

Of course local storage will be around, in some form. But my guess is that that form will just be a cache, and for some people, a mirror of everything on a small box (NAS/plugpc type device) at home, which they can take everywhere for convenience.