I have been doing a little reading on LED light, and from what I can tell so far, the reasons why LED light from displays is bad for our eyes is because it has a spike in the blue spectrum, it is lacking the infrared spectrum, and the switching on/off of LED's required for mixing subpixels (not to mention overall flicker from PWM dimming) to create colors. What I have been reading says:
Blue light has a short wavelength which easily penetrates to the back of the eye, causing strain and damage to retina cells with overexposure.
Infrared light is needed for healing cells in the eyes. And since there is a lack of it from LED displays, along with the strain caused by blue light, it is kind of like exercising your body to the point of exhaustion without receiving the required nutrients in order for your muscles to recover. In contrast, sunlight and incandescent light does include the infrared spectrum. So even if we are able to bring down the blue light to a sane level, the lack of infrared is still bad for our eyes.
On top of harmful blue light and lack of healing infrared light, there is the high speed flashing on/off of LED's which we cannot see with our eyes, but we can likely feel the effects of in our eyes in the form of fatigue and strian.
And going further, there is the possible negative effects of PWM, blurry font rendering, poor contrast for reading, effects of dithering, and glare from glossy displays.
In short, it seems that the cells in our eyes are being annihiliated in a number of ways.
Possibly most interesting is that light from candles (a very old technology) is much better for our eyes than realitively cutting edge LED light.