Travel. I can still look at my ToDos, email, note, saved stories (Instapaper) on a plane thanks to offline apps. I can use it as a clock/alarm/calendar while in another country. My phone can even be used as a GPS when offline thanks to apps like GPS Nav that allow navigation using saved map data.

Always-online is a luxury of spending all your time in certain parts of the world. Baking that assumption into all apps diminishes their utility greatly.