What about when you wake up and it's still dark and you don't know whether it's worth trying to go back to sleep?
In my opinion it’s always worth trying to go back sleep if you’ve got an alarm.
Speaking for myself, there’s nothing worse for falling back asleep than looking at the time. When I wake at night and it’s dark, it might be 11pm, 2am, or 5am. I don’t want to know what time it is. I go back to sleep and unless it happens to actually be within minutes of my alarm, I’ll fall back asleep and never know what time it was.
You could keep it under your blanket so you wouldn't need to move all that much to check the time.