If you remove the edge, you get a cylindrical display.

But wetness is the essence of beauty.

Quotes aside, I've imagined this kind of edgeless design to be where things are headed, and it certainly looks beautiful.

It's more likely that the next iPhone or Galaxy S will have the home button removed (finally), the speaker squeezed as far to the top edge as possible and the screen will fit all that new empty space, with 1-2mm borders.

That's doable in the next 1-2 years, this design isn't.