You still require the blue and red channels for green rgb output.
see:
https://upload.wikimedia.org/wikiped...eel_10.svg.png
Also you need to translate red and blue predominant rgb colors to green, eg. A red door becomes a green door with a filter otherwise that door wouldn't show very well in a green only output with red/blue pixels disabled.
Another point to make is that white's show up greenish on the Apple II monitor simply because there is no white. A filter would be required to translate pure white into green hue.