I do think America should invade North Korea. But not just America by itself. All of NATO. All of the UN. Anyone willing to form a coalition to stop the horrors of that nation. The thing is that North Korea has an extremely powerful military, and invading would be a tough road to travel.
Yes, America should invade North Korea, because we could get to where their nukes are stored sooner than they would be able to detonate one. North Koreans have suffered for how many years? But we don't do anything about it because they don't help the United States with oil and other natural resources.
America shouldn't invade North Korea. Instead, we should sic mercenaries and saboteurs on them, subvert them, and keep the Kims on as a puppet "all's well" government. From there, we can import German bureaucrats to re-structure the system. Bam, North Korea doesn't suck as much, first, because America, but also, German bureaucrats.
I think invading North Korea would bring about a huge host of problems that the United States doesn't want to deal with, the Chinese are allied with North Korea and don't want to share a border with South Korea so they use North Korea as a buffer, I highly doubt they would be too happy to see the United States invade North Korea.
North Korea doesn't post an immediate or imminent threat to the United States. If any country should invade North Korea, it's China. The Chinese started the rabble-rousing on the Korean Peninsula in the first place back in the late 1940s and early 1950s. North Korea is China's problem now since their northern border is shared with China.
I do not believe the United States should invade North Korea. At this time, we have no reason to justify such an attack, therefore it would be seen as a complete act of war. Since North Korea is backed by China, this would be seen as an invocation of war and it would quickly devolve to that state as well.