White and black are perfectly reasonable terms - I think most here understand the threshold at which grey becomes either black or white for general discussion.
Overall, reducing the contrast between the text, the background and the ambient light levels. The key here is ambient light levels. If you're reading in a darkened room at night, then a black background is usually very good, so long as the text isn't too bright, but in a lit office, for example, as I've demonstrated the contrast between the screen average and the ambient light is greater and that is likely to cause more strain.
To answer your question, I wouldn't use a 400cdm^2 monitor - no matter what, I'd turn it down (calibration is not the point). I *might* decide it was useful if I was trying to see something in bright sunshine I suppose, but more likely I'd try to shade the monitor and turn it down. In other words, I find that level of brightness too contrasted to any reasonable ambient light level I'm likely to encounter in normal events.
I'm talking about average environments in which people work and have reasonable lighting levels (200lx to 400lx).