You may have a point. Maybe ‘doing it quietly’, as you put it, leaves them alone with only their conscience, and no one to tell them it’s okay; to give them an ‘out’.
In fact I think you may have hit the nail right on the head.
Down to Brass Tacks - abortion is but one of the acts of shaking their fists in the face of God.
Without a “mob mentality” to support their rebellion,
it becomes, as you said, just between them and God. A very uncomfortable place to be in.