I thought about it, too. If we replace the hair with a hat, all males with that hat would look the same, and females too (except for eyebrows etc.) I think the head models have currently the hair attached, so for the moment would not even be possible.
There's other option, make the hat model with a default head attached, which would be useless due to the skin color.
I think the problem right now is that the hair that stands out of the hat should not be visible; in terms of 3D I think on boolean operations, but I don't know how Radiant will solve this headgear issue.
Doing it as a variant like eyebrows... I think I would get the same result as in the pictures I posted (they retain the hair, eyebrows and beards).