With these displays, there's not really an "off" because as long as there's no change on the display there's no energy usage. Of course, that dies not account for the OS.
I guess they could add some indication on the screen it’s in ”sleep” mode though, like a frame or icon somewhere…
I'm sure I'm underestimating the complexities of the problem, but the first idea that pops into my head is to add some flash storage that's, say, 5x the size of the framebuffer, and always keep in it the current page + next two and previous two pages (swapping pointers to avoid unnecessary writes), and have an extra microcontroller that would wake on button press, read the appropriate page from the flash buffer, and send it to the display controller. The whole process could take a fraction of the second (+ screen redraw time), all while the main OS wakes up (or boots up) in the background, and the user would experience no delays if all they're trying to do is read their book page by page. Once ready, the OS would update the flash buffer and stay active for a short while, in case the user decides they want to flip pages quickly.
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[0] - Gosh, I keep forgetting the readers only have touchscreens now. Another reason for superiority of hardware buttons for page turning.
Kobo still has a reader with buttons thankfully. I don’t understand how people tolerate touchscreen on e-readers. It’s extremely distracting compared to just pressing.
Buttons were absolutely perfect for this use case, on a dedicated e-reader—less so, say, an iPad mini that also does other stuff, but also those nicer touchscreens don't accidentally trigger as often so it's not as big a problem. Touch screen is nice for navigating menus but should be disabled when reading.