I think even if we went back in history we would never get this man to explain to us exactly why he would logically let this happen. Miller allows this charcter to prosecute these people to demonstrate what he thought Senator McCarthy was doing. It drives his point home. The sad thing is that this is based on the truth of the real deal Salem Witch Trials and it did happen.
Danforth's character reports that he will not pardon John Proctor in particular because Proctor will not confess to witchcraft (something he has not done) on a piece of paper by signing his name on a written confession.
Danforth was a man of rules and regulations, not of humanity. This was sort of the way it was with Puritans. Some of them got so caught up in following the regulations of their religion that they forgot entirely the concepts of grace and forgiveness that were also supposed to be a part of that religion.