The United States is not the final judge about countries around the world. There is no reason to start a war with North Korea, other than to prove that we can do it with impunity. North Korea has not attacked us or any of our allies in recent history. They bluster a lot, but that's all they have. The nation is so backward as it is, they don't need us dropping bombs on them as well.
North Korea is a very impoverished country. It could not sustain the financial impact of war. Furthermore, many of its citizens are victims rather than supporters of Kim Jong-un. If diplomacy efforts fail between the United States and North Korea, the U.S. should make efforts to remove Kim Jong-un from power either by force or through assassination prior to declaring war.
The U.S. should not start a war against North Korea because it is powerful enough in other areas that it doesn't need to resort to military action. War, especially in the case of the lone superpower versus a much weaker state, needs to be a last resort. If direct diplomatic efforts fail, the U.S. can engage China in the talks. It can also offer rewards for good behavior, rather than sanctions for bad, to bring about peace with North Korea.
The United States has already fought a number of wars including Iraq and Afghanistan in the past decade, increasing our military debt significantly. Unless national security is at risk, the United States should not be going to war against another nation; doing so could have dire effects on an already burgeoning national debt.