I'm not sure exactly how you're interpreting contract enforcement leading to violence, so I'll try to explain a little more. Two people make a financial agreement, hire lawyers, and depend on a powerful police force and and penal system to enforce the terms of their contract. This increases the need for armed police, prisons, etc. As more people and institutions are given the right to enact violence to enforce these contracts, people become more desensitized to violence and arrest and more opportunities for abuse present themselves. Abstracting this enforcement into software also distances the enforcement from the culture and removes some of the negative psychological effects on people of carrying out that enforcement.
That's on the smaller scale. On the larger scale, nations feel pressure into increasingly more arms races to keep themselves on an even level. Abstracting enforcement of agreements into software can have the same effect as the introduction of diplomacy into international trade. While it didn't eliminate war, it offered an alternative to straight-out aggression between tribes. Groups that used to stay to themselves and interact with each other only on disputed borders were able to cooperate on a much higher level by establishing representatives inside each others borders.
A smart contract system is a neutral, diplomatic ground for the Internet. Today, the Internet resembles in many ways the world before diplomacy. There is a persistent, escalating cyber-war between nations. People can move in between nations, but there's no real neutral territory that every nation would consider fair. By having a mutually-agreed and verifiably trustworthy software platform to enact contracts, there can be opportunities for new types of deals that are more mutually beneficial.
Will this suddenly eliminate war and hostility? Of course not. Neither did diplomacy. But almost nobody thinks we should go back to a world without any diplomacy, and once we have neutral and fair systems to conduct electronic business, few will want to give it up.