It's a shame that Kindles aren't hack-friendly, there are lots of old Kindles lying around that would be great as an always-on display.
Some Kindles can easily be jailbroken [1]. I have two jailbroken Kindle 4 devices and they're still great. Both for reading (though you have to sideload books) and as e-ink dashboards [2]. A Kindle 4 can run for ~ 28 days on a single charge, refreshing the screen every hour.
[1] https://wiki.mobileread.com/wiki/Kindle4NTHacking#Jailbreak