This might be a dumb question but how would named colors be more consistent across monitors? I thought they mapped to the same RGB value so there would be no difference between 'red' and #FF0000.
I remembered it wrongly. It wasn't about named colors, but "web-safe colors" that can be displayed by 256 color displays directly, without having to fallback to the closest color or by using dithering. Some of them happened to have a name attached to it. Don't know if the original 16 named colors are also all safe colors.
https://en.wikipedia.org/wiki/Web_colors#Web-safe_colors