don't you need to charge them eventually? so you end up taking them down a lot. they should think about wireless charging pads that can be installed into the wall for these sorts of things.
I wonder if trickle charging with a few calculator-type solar cells on each edge of the frame (not the face of the frame) would be feasible as well to prolong battery life.
But that requires a wire that goes from the outlet all the way to the charge pad though, right? I think the main goal is to have no visible wire when it's on the wall. On the other hand 7k image changes before going out of battery seems quite a lot. Just not sure if that's a representative number.
Even if you completely run out of power, the screen should stay on the last image it was showing. You might just see the same picture for days/weeks/several heat deaths until you decide to charge it again.
Just anecdotally I found it pretty fascinating that I bought a new Kindle some three months ago and it still hasn't run out of batteries (came with 76% and now at 16%).
My experience with Kindles is that the battery drain is all about wifi - if you keep it in 'airplane mode' most of the time (except to send new content to it / return library books early etc.) it can last for months on a charge.