As LME said, CRTs were dimmed to prevent screen burn-in. It was not recommended to turn off CRTs as continually switching them on and off stresses the high voltage circuits and could result in premature failure. Better to keep them running. This was true of most applications for CRTs, not just in cockpits.
LCDs are much more reliable and can be left on for as long as you like. I would guess that it is "good practice" to dim them when not used is either to save power by turning the backlight down, or avoiding the distraction of brightly glowing screens in an otherwise dark and empty flight deck.
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cj
-I wish life had a "pause" button