A monster is only as fascinating as its foe.
How impressive would it really be to see a predator slice and dice through a series of faceless drones, inner monologue or no? What does the audience gain? There is no suspense, no dread, no sense of loss, no sense of accomplishment. All you are left with is a montage of grisly death scenes peppered with voice over narration.
Could a predator be made into a relatable character? Perhaps, but it would take a lot to make it work to be done right, and a sense of accomplishment at defeating their foe would be one such quality. How do you instill such a quality? You flesh out the quarry to make it not a something, but a someone. Without that, you are left with
"The predator killed...that guy whose name I don't know. But he wore a nice suit so he must have been important! Oh, and the predator it talking to himself now!"
You need more than one face to make a story work. Predators fixate on their prey because they know their prey is worthy of them. The audience should be made to feel that, and without a developed character, it can't be done.