Computer monitors cause eyestrain for two main reasons: they require the user to stare at a relatively short focal distance for long periods of time, and they're quite dim compared to daylight. I propose solving these two problems, in hopes of making monitors easier to use.
The second problem is
the easiest: use a brighter backlight. As bright as the daytime sky seems appropriate. This will help stimulate the suppression of melatonin production, making users more alert. Of course, it would be prudent to decrease the brightness in the evening to allow the user to sleep with less trouble. Adjusting the colour temperature would help too.
The first problem is a bit more difficult, but I see two possibilities. The simplest is to put a big glass lens in front of the display. This will allow an infinity focus to be selected, approximating staring at the sky.
Of course, such a large lens would put us back to the CRT days of weight and desk space usage, not to mention the high cost. Instead, how about a lenticular lens? They are often used to give silly 3D effects, but in this case it would be fixed to infinity focus.