Why? So you can accidentally tap the screen every day with the edge of your fingers as you hold the device?
It's why I don't quite understand the Galaxy Edge.
What was really interesting is that the Moto physical design almost seems like a premonition of today's notched displays and thin bezels. If you built it today but removed the bit of border at the top and bottom of the screen, you could cram in even more screen. If you also made it just a few mm wider, I think you could make a great compact phone with approximately 5" screen.
I think the side bezels could also be half as thick, as long as they were a slightly raised. I think you could also disable the touch sensitivity in the very edges of the screen without compromising the UX. I want to see extra pixels for border around text, etc. but I don't really need to be able to click or drag the border itself.
There's room to gain some extra vertical real estate, though it would presumably involve getting rid of the home button and going with a notched screen. I'm ambivalent about the desirability of either option from a pure hardware perspective. I like being able to get a secure grip on my phone by putting my thumb somewhere that isn't touch-sensitive, especially when I'm doing something like trying to use my phone on a crowded train. But, where so many UI people (including Apple's own) have taken to being actively wasteful of vertical real estate these days, I can also see where it might still be a net positive insofar as it would mitigate some of the UX damage they've been doing.