I found some iPhone cases on Indiegogo​ ​​ ​
that carry an E-ink display on the rear. You can check the time and schedule, even the weather forecast without checking separately or having to launch the iPhone. It seems also able you to check the web. Because it is E-ink power consumption is small.
In fact, as there is little that is actually displayed, it means you don’t want to use as much.​ ​
I am looking forward to having one.