Because in Lord of the Rings, Eowyn effectively is interested in a guy who’s above her, not only in the aristocratic rank that supernatural boyfriends can be a stand-in for, but also in the sense of having (admittedly fairly distantly–but not so distantly it doesn’t affect his lifespan) elven blood. And like in many paranormal romances, she’s convinced she cannot live without this guy, and wants to die, quite literally in her case.
But she doesn’t take that depression and despair and languish around bemoaning her fate, assuming she can do nothing if he doesn’t love her. She takes it and goes out and decides that if her life isn’t worth living anyway, she can at least join the battle against the forces of darkness and do some good before she dies.
And of course, she doesn’t die, and because she doesn’t die, she has time enough to get over that guy she thought she couldn’t live without–who, as it turns out, was holding out for a supernatural girlfriend of his own, one more powerful than him and above his station, and that was the destined love Tolkien was aiming for, because unlike in paranormal romance, if LotR is intended as wish fulfillment, it is not girls that it’s wish fulfillment for. (For all that generations of girls have found it there just the same.)
But Eowyn moves on, as one does in a world where most love isn’t destined after all, and falls in love again–not in a settling for second-best sort of way, but with a guy who is truly worthy of her love, arguably more worthy than her first mad crush.
And she lives happily ever after in the world she helped save.
I have other issues with Eowyn’s arc (for all that I ship Eowyn and Faramir like crazy), but all told, that’s not a bad model for how a paranormal romance can go.