Women weren't much employed at police departments and mainly worked inside as glorified office workers, never on the streets. The idea that one of their girls would demean themselves to play a prostitute was unthinkable. So "real" officers (aka men) played those roles. These days, with women on the street, on patrol, pc detectives, etc., it's not hard to recruit female officers for those uc roles.

I was actually recruited to allow the PD to check off a box on the compliance forms. In fact I was a "twofer", not only their token female but also a lesbian - two checkboxes. (There was no checkbox for trans then.) That didn't make life any easier, I was a means to an end, nothing more. Like Rodney Dangerfield, I couldn't get no respect.