If you don't refresh it too often you could run the display for about a week from a 10000mAh powerbank. Of course then you would need to run it from a microcontroller instead of the rather power-hungry Pi.

It's doable today, just not convenient.

Actually yes - I have a small display that I haven't used for a couple of months and the image is still there. I was thinking about how it would be with a daily refresh.