This sort of brou-ha-ha is one of the reasons the Jockey Club still requires both the participants to be present and accounted for . . . I guess letting the young folks have a good time is another.
Plus of course the ever-present risk of fraud. DNA typing has made it a lot harder, but jugged semen is a . . . ahem . . . fertile field for con men.
My current horse used to be a broodmare. She is the easiest horse in the world to load on a trailer - you just open the door and in she goes and stands to be tied, 'cause she's all starry-eyed thinking she may be headed for Romance.