OLED works with TVs because larger displays more frequently have problems with shit like clouding, input lag (they're TVs), backlight bleeding, TFT glowing (like IPS glow), and so forth. Plasma TVs will give people the shakes with its reputation for burn in so that's a no go for a lot of people. Full array TVs have good black depth but have problems with haloing and input lag so that's a pretty bad solution for a lot of people. OLED circumvents most of these problems: there shouldn't be clouding, there shouldn't be any distracting off-angle glowing, input lag could potentially be lower (though doubt it if its scaling), backlight bleed is a thing of the past, etc etc. It will still have burn in problems but for a lot of people that's not a problem. Things like oversaturation and bad default calibration aren't too much of a problem because with a high end display, you're going to calibrate it anyway.
Now do those things really apply for small scale displays on mobile devices? No, not really. Backlight bleeding is a problem but most of the examples you see (like the S4 example above) is a result of camera overexposure to help show the problem areas. All of the other stuff is basically a side effect of having larger panels, colmplex electronics, or some crazy backlight array.
Really, the only areas that OLED wins is in black depth (which is obviously important for TVs) and theoretically motion performance if that really concerns you. To be honest, this is a phone and I'll currently take a little bit worse black depth for some half decent colour accuracy, greyscale performance, and less chance of burn in.
