Phones produced for the Japanese market are usually so radically different than the ones we're used to that you don't really feel like you're missing anything. However, the new Sharp Aquos Crystal may pique your interest. The difference is that you might have a chance to buy this one soon. This device comes in two sizes—5-inches and 5.5-inches. Both of them have teeny tiny, miniscule bezels. Almost none of the body peeks out from the edge of the screen.
It's Bloomberg though - they're reliable. They can't be wrong, right? They say the phone "uses the entire front of the device as a display," and "maximizes the screen viewing space by eliminating the black frames or bezels around the display." Several times they use the phrase "edge-to-edge" screen.