It'd be a nonsense to refer to the lines by colour anyway, not least because many people are colourblind so you'd have disability issues with so many shades of similar colours in use.
But also you'd have a naming convention which is as boring as the LA metro which does exactly this, i.e. it has a 'red line' and a 'green line' etc. - who wants that??
Yes, indeed a quick google seems to suggest quite a few US cities do this - Washington DC, San Fran, Boston and Atlanta and maybe others. Not NY obviously.
I do think the tube would lose a bit of character if we did the same.