Radians are the SI standard unit of angular measure.
Are they? SI may adopt them as standard, but no particular set of units is necessary to define a radian.
your initial question really got me thinking about the whole thing again, been a while since I actually used mils, and even then, that was under the pretext of the U.S. Army - and a brief stint using a Zeiss.
But they are dimensionless, by definition, like sine and cosine.
The only reason they really got into SI, is its reliance on base 10, and the ease of 1 meter over 1000 meters (or 1cm over 100m (.1 mil))
but it works just as easy with 1 ft over 1000 feet. You start getting goofy when you go to inches over yards.