For starters you can use it as a compass (anologue watch) if you learn how.
If you travel across time zones, you can work out your longitude. (again if you learn how)
If you know your walking pace, you can work out distance traveled. (or other speed)

You might actually need to know the time for some reason. You dont have to estimate from the sun, and you can tell the time at night.

If you have a radio and you are in a disaster, you can listen to the 3 oclock news when its 3 oclock, not wasting batteries listening to the radio all the time.( or any other important broadcast)

There are heaps of reasons and these are a few than flew into my head.
But it is your choice.