I think everyone would stop having conflicts if they knew it would lead to world peace, but they know that preventing one conflict won't stop all of them, so they continue to have them. It's like helping the environment. If one person was in charge of all pollution's and you told them that if they were to stop, then global warming would end, they would stop. But let's be real, one more person recycling their water bottles, isn't going to save the world, hence why it isn't such a big thing.