Well, I think this is much more of a viewpoint thing. The regular people of, say, Caldeum want to believe they live in a new, perfect world and the demons are a thing of myth (which is why they think Cain is a psycho- he's the one telling them to be ready).
It could be like in The Black Road: I think I remember reading that demons were scarcely seen by the people, but lo and behold, there were men and women like those that group together with the protagonist to kill Kabraxis that would go and find them, anyway.
In Legacy of Blood, there was never a *large* insurgence of demons unless there was a hero born to counter them. Some kind of theory or something. It's been a few months since I read it.
So... I agree with others here that believe there doesn't need to be hordes of demons on the mortal plane for there to be Demon Hunters. We don't have serial killers all over the place, but we do have people that are affected by them now and again.