True, but the shiriffs only showed up after The Hobbit got absorbed into the Middle-earth mythos. So the term "policeman" itself does sound out-of-place, even if the concept of a shiriff exists. I think that "police" to mean "law enforcement" is a more modern term and thus gives a more modern connotation. (Also, "shiriff" makes more sense for the Shire from a purely etymological standpoint, since "sheriff" is itself a worn-down version of "shire-reeve," and it comes from English rather than Greek.)