I have to have an analog clock within sight in the morning. When I first wake up I'm too tired and bleary eyed to think about numbers but I know what angle the minute hand will be at when I have leave to catch the bus to work. When you're familiar with an analog clock it's far more user friendly than looking at some numbers and have to do some math. Sure it's simple math, but first thing in the morning, I'd rather just glance at the minute hand and when I see the angle I just know.

So I don't think it's not going away despite it being obsolete, it's not going away because it's more user friendly. Sure there's a learning curve, but once you've gotten the hang of it, it's a more efficient way for a human to get a sense of time, which in many cases is more important than having a numerical representation of time.