Interesting. It's basically a compromise between flicker and motion blur, so I assumed they'd pick the phosphor decay time based on the refresh rate to get the best balance. So for example, if your display is 60 Hz, you'd want phosphors to glow for about 16 ms.
But looking at a table of phosphors ( https://en.wikipedia.org/wiki/Phosphor ), it looks like decay time and color are properties of individual phosphorescent materials, so if you want to build an RGB color CRT screen, that limits your choices a lot.
Also, TIL that one of the barriers to creating color TV was finding a red phosphor.