The only apparent advantage is they can make the device thinner and call it a 5.7" display, when from a straight forward video view it is really 5.5" due to the curve. The display feature used is just a little swipe strip that can be done with a flat display. The curve is not needed for that.
I get why Samsung did it (S7E sales), but seems if people wanted a curve they would buy the Edge (for less). The combo of the edge display, 820 and high price might sway more people away than gain. I tried to like it, but the display IMO is less user friendly due to harder to case protect, video distortion for media and awkward while gaming. Not conjecture either, since I tested one out today. Love the pen function though, but that is about it.
As far as the 820, they kind of had no choice unless delayed to give chance for 821 production ramp-up.