Let's face it: these movies aren't really about the fear the world has of the Antichrist which will be its scourge. These movies are about the impact of a stranger's child on nice, decent, well-off couples with fertility issues. In them, we don't see the Antichrist grow up and rule the world and bring it closer to destruction. We see families suffering through the early stages of raising the Devil's spawn.
There is something about the Unknown that makes it fertile ground for fear or fantasy.
The "birth mother" could so easily be an addicted demented teen. The "donor" could so easily be a sleazy, amoral creep jerking off into a cup while looking at cheap porn for a small allowance. And so the child could so easily be just like his parents, although we choose to believe that we will be his only real parents and the only ones to impact him in any meaningful way.
We are told to believe that. We consciously might even believe it. But our collective unconscious seems to break out in movies such as these. The overwhelming fear of raising someone else's child, who might be sired by the Devil himself, for all you know, has to break out somewhere!
Isn't it only rational to imagine that parents who know that they don't know their child's parents will constantly have fears and doubts about the child they're raising? That every time the child misbehaves, or displays a difficult trait, or does or says something strange, the parents will see that Strange Other in the child and retreat from it in fear?