It's pure history. In ancient days the early cave-graphics programmers thought of the monitor (teletype? stonetype?) viewing surface as two dimensional graph paper. In math and engineering the usual conventions for plotting data points on graph paper is: x=right, y=up. Then one day, about a week after the invention of the silicon wheel, someone thought of 3D graphics. When the candle-bulb of this idea blinked on above their head, for whatever reason, they choose to add Z= away from viewer. (Ouch, my right hand hurts just imagining that.)
They had no idea that someday their far descendants would become engineers, scientists, fine artists, commercial artists, animators, product designers etc and find 3D graphics useful. All these fine modern people use right-handed coordinate systems to be consistent with each other and the more established math texts and physics conventions.
It is foolish to base the 3D coordinate system on the display surface. It's the model that counts - the triangles and polygons and planes describing a house, chair, overweight green ogre or galaxy. Nowadays we all design and model stuff in right-handed XYZ systems, and do so in terms of the model's world, even before thinking how it'll be rendered. The camera is added at some point, possibly made to fly around in crazy ways, and it's invisible infrastructure that converts the model to pixels that within its bowels must twerk around with coordinated system transforms.
Just to add to the confusion, some graphics libraries recognize that CRTs scan the image from top to bottom, and so have Y=down. This is used even today in all windowing systems and windows managers - X11, fvwm, gtk+, Win31 API, etc. How new-fangled 3D GUI systems like Clutter, Beryl etc deal with Z, is a separate issue from 3D graphics modeling. This need concern only applications programmers and GUI designers.