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What could be really cool with a flexible display would be capacitative buttons on the top edge (i.e. places you don't usually hold the phone). Would be nice for the volume rocker, as well, because thru a case it can be a pain to adjust effectively (this assumes the software handles incidental/unintentional touches).
Obviously, then, you can't have a case if you have a wrap-around screen and little to no bezel...so the phone itself would have to be pretty rugged
Samsung should just make the same stuff but in different sizes. Have phones with a 4" & 5" screen, a "phablet" with a 6" screen, and tablets with 7" & 8" screens. All bezel-less, of course. Problem solved.