Adding geopolitics into the mix will give you a slightly different story. Nobody in the region would benefit in any way from warfare at this point in time.

The United States can drop plenty of ordnance on North Korea, but could in no way follow up its air strikes with a ground war.

War would create a huge amount of instability for North Korea, and despite their massive army, they lack the strategic capability to project their power beyond the Theater. North Korea can expect almost no aid from other nations(certainly not from China, who is very cozy with the United States economically), but has plenty of enemies in the region that would jump into a coalition against them, more out of necessity due to the North Korean total war strategy of unleashing both conventional and chemical attacks against major population centers in the ROK and Japan.

For the reason stated formerly, Japan and South Korea would have a definite role in any war against North Korea. South Korea actually has greater interest in keeping the North a separate nation; the culture, values, mannerisms, and even the linguistic dialects of each nation are different than they were pre-1950. The instability that would be brought about by a conflict won by EITHER side would create monumental problems for either government. Assuming the Korean War ends, the ROK has to deal with potentially millions of hungry jobless North Koreans swarming South after the borders open... Despite what some may say, the Cold War status quo of ceasefire is still much higher on the list than war or peace.

Military aside, the political fallout for the US is undesirable enough that American policymakers will continue to keep the status quo over peaceful resolution or warfare. The loss of two key regional allies, potential fallout covering a very large area, and the worsening of relations with every other regional player that would follow, basically keeps both sides rattling their sabers, but won't likely see a conflict unless a serious accident happens. The North Korean government is not crazy. They are sane enough to know that any war they fight would likely end in loss. What they also know, however, is that they can make a war so terrible that nobody would ever seriously think to attack them without permanent consequences.

Like an evil version of Switzerland almost!

RRR