When it came to extras, wouldn't there be a greater advantage in reusing costumes, the fewer colors there were? If the color scheme was too specific, then they couldn't, say, reuse a security extra's costume on an engineer extra in another episode.
By the way, if the idea really was to sell color TV's, as I've heard, then three colors, one for each primary, or at least spread out in color space, is the bare minimum you need to show off color.
Both those considerations together would imply a three color scheme as the optimum number.