The very thin ereaders have a cut-out in the alloy chassis for the Li-Poly cell which rests against the screen. That's what the not actually very thin Cover Story had. The recent Kobos I've examined have alloy chassis over entire pack of screen, with just reinforcing ribs missing from casting at battery (really a cell) location so that it can't damage the screen. I call that a premium design
The cells often swell with age anyway.