[citation][nom]grndzro[/nom]What's preventing a standard LCD from being on the side of a phone?[/citation]
LCDs are rigid, if you want an LCD on the side, you have to add the whole thing including backlight, panel driver and all the other support stuff.
With bendable OLED, you simply use a slightly larger screen and bend the edge. If you were going to use flexible OLED due to shatter-proof properties, bending it for edge display comes at nearly no extra cost nor complexity.
As far as cost goes, I am quite confident OLED will get much cheaper as processes and materials mature. Silkscreening or inkjet-printing OLED panels (the holy grail for OLED manufacturing) would be much cheaper than the high-temperature vapor deposition process used for LCDs.