While the general idea is laudable, the simple statement that vampires can’t exist because they’d have killed all the humans is just stupid. In summary: if a vampire feeds once a month and creates a vampire of its prey, then there would be no humans left. So we’re either all reformed vampires, or they don’t exist.
Surely it’s more fun to speculate that there is a vast, undercover army of vampire hunters who are protecting us from the vampire population explosion we all fear?