Create (I)phone case with a LCD clock down one side

I had a silly idea (no such thing)

People who use their mobile phone use it to check the time many times a day, they also wake up and check it in the dark.

I’m thinking would it be possible to build a case which has the time displayed down one side of the phone, runs off its own battery and has no other features but to tell the time.

The phone could be placed on the desk, bed side table etc etc and the time would be visible (light but not too light)

Idea and probability of being able to make such a thing and also argument against it too?