This is something for which we can't blame Stephenie Meyer. Her heroine is, at least, just the daughter of the local policeman. She might land herself a hot vampire boyfriend (or should that be a cold marble-skinned one?), but she isn't a vampire princess or a chosen one (at least - not in the first book. I haven't read the others yet).
I have just received my latest novel in which the heroine, a "normal American teenage girl" suddenly finds out she's a princess of some supernatural realm. I made myself read something else first, so that I wouldn't be biased.
But there's also a new pile of books at my school, to be processed next term, with at least three of these books in it. I think one of them is about a girl who finds she's a Faerie princess and gets a hot boyfriend from the supernatural realm. Vampire princesses are common. The story is as follows: the heroine is about to turn sixteen. She finds out that her parents are not her real parents, or at least her single-parent family is that way because her mother once had a romance with a vampire, a demon or a Faerie. And the father is always, always a king or a prince. Which makes the heroine a princess. And if she doesn't date the gorgeous mystery boy who has turned up in her life, the world will come to an end. Usually, there are bad guys after her, wanting to use her specialness for their own evil purposes.
Buffy, please come back! She may be the teenage "chosen one", but at least she's not a princess. And before the series was over, she found the reason for the "chosen one" and made damned sure that every girl could do what she did.
But, all this said, for the time being at least, the girls love it. So we older cynical girls will just have to accept it.
On the other hand, at least one of the good readers in Year 7 at my school has asked for the original Dracula. She too is getting a little tired of the vampire princesses.