The need for human blood is not, really, about food. It's about antibodies.
The vampire's immune systems have come to function in a completely different way from human immune systems. This has allowed them to enter into a symbiotic relationship with several bacteria that block cancers, promote muscle oxidation at amazing levels, allow stem cells to rebuild the body repeatedly, etc.
Only the vampire is unable to regulate the bacterial growth. The same immune system that allows them to tolerate the bacteria renders them incapable of resisting them. With enough time, the bacteria will flood the vampire's body and eat them alive.
The bacteria, however, are harmless to normal humans, who are universally immune to it. The various symbiotic bacteria are related to a common gut bacteria and everyone has antibodies to it. These are the same gut bacteria that cause people to develop antibodies to A & B antigens on human red blood cells. Animal blood has antibodies, but the vampire's immune system recognizes animal antibodies as foreign and rejects them, while tolerating human antibodies.
Whenever the vampire senses the bacteria are growing out of control, they are compelled to seek out human blood. While the vampire can't make the antibodies, they CAN use them. The more human blood a vampire consumes, the more the bacteria are in check, and the more "human" the vampire is (tolerating sun, ordinary strength, possibly even aging). The less human blood the vampire uses, the stronger and more vampiric they get (right up to the point where they die of sepsis).
This does mean the vampires would have a unique vulnerability or gift - antibiotics. This could be anything from a replacement for blood (the wonders of modern science) to an acute vulnerability (drink the wrong victim's blood and your bacteria die, and then YOU die). This can be whatever you want to make of it story-wise. Eventually, the bacteria will develop resistant strains and the antibiotics will stop working.
This also means that blood type could affect the vampire. Perhaps O blood is the universal treatment, but B blood (alone) leaves powers more intact (yet only as a temporary fix), and A blood (alone) weakens the vampire while not entirely satisfying their needs.
It would also mean the vampires could get everything they need from blood by using/consuming/transfusing plasma. In the same way modern medicine uses convalescent plasma to treat infections, your vampires just need the antibodies. Eventually, this will allow vampires to take synthetic antibodies and skip human blood altogether.