The Next Evolution in Small Screen Design: Bezel-Less Screen
rikacomet.blogspot.in
rikacomet.blogspot.in
Seokwon Hong's original design, did take care of that problem by leaving margins in each app, that are un-interactive.
Another solution can be minimized mode, where the device uses 90-95% of the screen in normal phone mode, and 100% (no margins) when attached to other screens.
Having a virtual frame is fine, especially if it were designed to display content like the current time, notifications and maybe feed data. You could still use the capacitive surface in that space to support edge-swipe style gestures, and you could allow apps to go "fullscreen" when warranted (for games and content like movies).