Edit: Also Hideo, no one has EVER started a war and had the money to fund it. World War II alone put the U.S. nearly 4 trillion dollars into debt (Adjusted for inflation to match today's rates). The point of a war economy is to stimulate industry through spending and employment. Money never just "disappears."
If you look at the WWII debt as a percentage of GDP the debt we accumulated would be around 16.8 trillion dollars. While this isn't the correct monetary value of how much debt we held, it is a good measure in the practical sense of how deep in debt we were.
Does that mean the USA is soon gonna go "HURR TIME TO GO PROTECT OTHER COUNTRIES EVEN THOUGH WE DON'T GOT THE MONEY FOR IT!" ?
While the Iraq war was of debatable utility, for us to refuse to honor a mutual defense pact with a nation that we are allied with, like South Korea; would collapse the US economy much quicker than accruing excess debt ever would.
If we reneged on a promise of that magnitude, no one would trust any other kind of promise we would make, such as the promise to pay back our debts.
This a completely different situation compared to us invading a country.
While North and South Korea have a storied history, the backlash if we refused to help would be like if we refused to help a European ally or Canada if they were invaded.
Honestly, I don't see DPRK intentionally starting a hot war with South Korea and the US; though accidentally starting a war by some over exuberant action of a group of soldiers on their side is a reasonable possibility.
What remains to be seen is if the spiral into war could be stopped before it escalated too far.
