I disagree. At its root, all the Edge really is is a software trick. There aren't physically two separate screens, just one screen that curves around the edge and is considered by the phone's software to be something separate from the main screen. If you use the one handed operation that shrinks the entire screen down in order to be able to use it with one hand, you can see that you still have all the functionality of the edge screen, but it's no longer along the physical edge of the phone.
There's no physical reason you couldn't have the exact same functionality as the edge has on a normal phone. I'm not saying it's not useful, but let's not kid ourselves. There's nothing special about the screen itself that makes it physically impossible to have the functionality that the edge has on a normal phone. Sure, it may not be as ergonomic to use on a normal phone, and functions like the ruler or the night clock may not make as much sense on a phone with a flat screen, but it's physically possible to do it even without the curved screen of the Edge.