I read for an hour or two before bed every night. Paper, kindle, or my current iPad mini make no real difference to my sleep.
Dim lights, relaxing, and trying to clear my brain of distractions other than what I’m reading make more of a difference. It’s almost but not quite like meditation.
(And then it wouldn't be that surprising I don't think if we figured out splints long before anything you might call medicine.)
You can switch out broken bones for „being dragged from the campfire into the dark and devoured“ - another natural occurrence that I gladly live without
(I think the science behind blue light being bad for us is still up for debate, but it's hard for me to ignore the amount of anecdata I've heard, including my own experience using flux and the like)
Would be interested in studies refuting this.
Anyway, LED backlight shouldn't be a problem if it's not white light. Best to have some additional light in the room though, to reduce contrast / eye strain between the screen and the background.