In the 80's I were one of those that played games on CGA mode in a green phosphor CRT and loved it. Seeing CGA games today on all their real color "glory" don't fell like the real thing at all to me. It's like green (or ambar for that matter) was "The way it was meant to be played" all along Very Happy
I would find this to be very odd indeed. CGA stands for color/graphics adapter , which means it was designed for color monitors using a digital TTL RGB encoding @ 60Hz. There were better cards, the MDA and Hercules, that could be used with digital TTL monochrome monitors. They used long-persistence phosphors to reduce the flicker at 50Hz.
Now, CGA adapters cannot use mono displays and MDA adapters cannot use color displays. However, this assumes you are using IBM hardware. There were clones that supported both MDA and CGA standards and supported both types of monitors. To use a CGA modes on a monochrome monitor would require the card to translate the data into something the monitor can display.
However, there is an easy way to do monochrome CGA, use a monochrome analog monitor, which the Apple IIs used. Works for every CGA mode and CGA does assign unique luminence amplitude values to each of the 16 colors in its palette. All this requires is full composite color CGA support, unlike the halfway support currently available (but for that to happen there would have to be a composite CGA mode added to the adapters DOSBox supports.)