This is a neat idea in theory, but overall I see it as a huge step back. The big cons here that really kill this browser concept are:
1. Home computers are not always on, nor are their connections optimal or secure. Everything that occurs here is at the behest of an individuals PC and all of their personal and local settings, and at the mercy of everyone they connect to.
2. If your home machine crashes, if a hard drive dies, etc...then potentially everything is lost. Gmail will always have your email...Youtube will always have your movie...but your home machine may not if a hard drive fails.
3. Security will be a huge mess. You're allowing tons of access to your personal computer while accessing many others in a similar way.
Opera has always been a fringe browser used by geeks and computer science people with a desire for an alternative, and faster browser. It's never been mainstream and these changes are not going to change that. If nothing else, average users that try it may very well open their computers up to even more security issues.