There was a brief moment around the turn of the millennium where that was what some of us were expecting. I was in college just after that and there were some free Internet kiosks, which combined with the ubiquitous free-to-use computer labs on campus, did a pretty good job of making this type of lifestyle possible, to the extent you could store your important documents online (much harder though in a pre-Dropbox, pre-Google Docs world!). Or another thing that was a big trend then was Portable Apps. On a flash drive on your keychain, you'd have installs of apps that you needed, together with their data and whatever documents you might need.

There was a brief period before that where some airports had pay phones with text terminals and modems built in, so you could dial up your corporate email or CompuServe. I swear I did not dream this.