You mention pelagianism as an example (along with its many flavors or variants), or semi-pelagianism as well, the common denominator with the governmental or moral-influence theories of the atonement could be its man-centeredness. It could be said that there are two views of Jesus in the world and throughout history: One being Christ's vicarious, substitutionary atonement and the other recognizing that Jesus was a good person (which is undeniable) and therefore His life showed us a better way to live. A moral example for all men and his death, an example to deter men from doing bad things. All religions acknowledge the moral superiority and example for men. Only one view recognizes that He was the only person who could provide the propitiation for man's sin.

Machen does boil the 3 views of the atonement to only 2: Man-centered (moral-influence and governmental) and Christ-centered. See Here: The Bible and the Cross

The Chestnut Mare