This reminds me of the whole "web operating system" or "web desktop" trend [1]. It was pretty hot around the mid-noughties, or at least that's the impression I got, but peaked in 2007-2008 without having produced a killer app (tellingly, nowadays Google Docs and the like still don't offer you a "desktop"). I tried quite a lot of web operating systems at the time -- mostly to see just what they could do within the browser -- but, frankly, couldn't find much of a practical use for them except to mirror my static websites on the free webhosting with high disk quotas that many generously provided. At least one, YouOS (YC W06), got venture funding but even their product didn't work out (they pivoted -- successfully [2]).
Come to think of it, the way those systems got around the limitations of the browsers at the time made some aspects of them pretty strange. One I remember in particular integrated a real office suite with their Ajax apps thus: it had a Java VNC client with which you accessed OpenOffice.org running on their servers.
If you're interested in the history of the subject try exploring http://www.crunchbase.com/tag/web-os.
[1] See https://en.wikipedia.org/wiki/Web_operating_system and https://en.wikipedia.org/wiki/Webtop.