Careful that you don't undermine your own point here. What Milgram demonstrated was that authoritarianism works.
Experimenters like Milgram and Zimbardo were trying to illuminate the motivations and mechanisms of the Holocaust, an event that could have been stopped by the moral authority of religious leaders including the Catholic Church but was not. Instead, what happened in their constructed scenarios was not that different from what happens in a church: an unaccountable authority tells ordinary people to do debatably-ethical things in order to achieve a goal or carry out an assigned role, and a majority of the audience is receptive to these orders.
The only surprise is that someone actually had to do an experiment to remind us just how gullible we are.