There's an article in the book 'Nature's Body: Gender in the making of modern science", written by Londa Schiebinger, that talks about the factor of race in beards men had. "Though debates about skin color dominated eighteenth century anthropology, some naturalists, notably Charles White, felt that hair, its color, texture, and length, had not been given the attention it deserved for differentiating the races. The beard, in particular, took on special significance. The presence of absence of a beard not only drew a sharp line between men and women, it also served to differentiate the varieties of men." page 120. The chapter goes onto list different cultures around the world at different times and the individual importance of beards. Keep in mind, however, beards were seen as improper or lazy in Roman culture, so it couldn't've been a hugely easily accessible removal process as you suggested above.

EDIT: I would post the article if I knew how, but I think I've cited it rather well. If you have access to JSTOR it should be fully available on there as well.