I try to create lots of theories using different possible causes.
Here is one of them that makes me most sense.
Some people here also think it's pupil related
Unstability in pupil reaction (contraction/dilatation) that leads to over stimulation in eye muscle-optic nerve-brain
The exactly mechanism and precision of pupil contraction is not exactly know. And i am not doctor, so I barely understand anything.
Neverthless, from what i read, there are at least 2 mechanisms, that the pupil/brain used to control the size of the pupil. Cones receiveing light and photosensitive retinal ganglion cells (pRGCs).
pRGCs is used to stabilise pupil contraction. Then the pupil is also using Cones (photoreceptores sensitive to color s(blue), m(green), h(red)) to control the size of the pupil.
In a spectrum even-equal, those cells, just stabilise pupil contraction trough pRGCs. The most sensible part of this cells is on the wavelenght of 470-490, being 480, the most sensible. This is precisly where LED's have a lack of. The LED's blue light spectrum is strong around 450-460 and on 470 is low and 480-490 is almost non-existant. So the pupil cant stabilize properly. In CCFL it's better but not perfect, the wavelenght is not also even.
So it might happen that the actually the pupil is letting more light than was supposed to, because it's more open than it should, because there is no proper 470-495nm wavelength on Led's. (slow building of strain). Light at 460nm elicits only half the pupil response of light at 480nm. Published by PCM, a paper by Zaidi, Hull, Peirson. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2151130/
(off topic: how do i insert images here?)
Also the pupils can use the cones to get feedback of the light entering. So it relies on those changes of color to try to choose the aperture of pupil.
If there is flickering/dithering the pupils might contracting/dilating at a fast charge, or the brain might become stressed, overwhealmed because is being excited of constant changing in colors at a fast frequency. (20hz-100hz) Nature is not really color changing flickering in this rates. We dont see outdoors colors flickering this fast, or dithering.
We might be really sensitive to changes in color. Any slightly change in color the pupil is contracting/dilating. (Fast feeling of eye pain, and neurological symptoms). The higher the brightness, and so color contrast, and uneven of spectrum the faster, the faster the process.
So maybe we cant control/stabilize the pupil because of lack of part of the spectrum, and also we might be or oversensitive to cones<->brain processing, or have a lack of cones<->brain processing.
Maybe because we are oversensitive to cones color changing our brains might rely more on the photosensitive retinal ganglion cells (pRGCs) to control aperture.
Also from some of us who are eye-convergent, the brain found it easier and learned to rely more on those PRGCs cells to control aperture. And so it get used to.
So when using Led's displays is safe? When there is low brightness of the display, and almost to none flickering of colors that make our eyes/brain become unstable.
So there are 2 things to indentify the lack of quality of a display.
1 - The difference between the amplitude of the 470-495nm region and the maximum average bright are of the display.
2 - The flickering of colors. White is also color (the 3 primary color at same amount).
This is widely speculative.