Institutionalized torture in Christendom was not just an unthinking habit; it had a moral rationale. If you really believe that failing to accept Jesus as one's savior is a ticket to fiery damnation, then torturing a person until he acknowledges this truth is doing him the biggest favor of his life: better a few hours now than an eternity later.
Why should the spread of ideas and people result in reforms that lower violence? There are several pathways. The most obvious is a debunking of ignorance and superstition. A connected and educated populace, at least in aggregate and over the long run, is bound to be disabused of poisonous beliefs, such as that members of other races and ethnicities are innately avaricious or perfidious; that economic and military misfortunes are caused by the treachery of ethnic minorities; that women don't mind to be raped; that children must be beaten to be socialized; that people choose to be homosexual as part of a morally degenerate lifestyle; that animals are incapable of feeling pain. The recent debunking of beliefs that invite or tolerate violence call to mind Voltaire's quip that those who can make you believe absurdities can make you commit atrocities.