China has made it clear they aren't particularly thrilled with the idea of having someone not under their thumb next to their border as well. As a consequence of that... the "best" scenario would probably be China invading. But "best" is definitely in scare quotes as that could go VERY wrong very very quickly. I think the PRC is aware of that too. So unfortunately that means the DPRK will starve, because the realpolitik is such that solving the issue is just not a tenable solution for all the other parties.
On the other hand, the current costs of hostilities isn't free either as militaries don't pay for themselves; e.g. a 10% decrease in military spending for countries like South-Korea and Japan would save billions every year (right now, both are increasing spending).
I agree it's not a simple situation because there are 25 million mostly uneducated starving North-Koreans you've got to do something with, but in purely financial terms you're probably going to save money in the long run.
Part of the problem is that threatening North Korea plays into the hands of the Kims - it makes the "strongman leader" more attractive.
Invading Iraq and tearing Libya to pieces really didn't help.
I'll also point out that ROK and the US maintain 24/7 surveillance of NK depots and munitions storage areas (and pretty much everything else). NK could not attempt to mount such an operation without being detected. Unless they use their 100 year old stealth biplanes, then all bets are off.
It's just a single branch of military, quite useless if there is modern missile-based air defense in place.
One of the big problems has long been that North-Korea has a large network of artillery within shelling distance of Seoul. Now they also have rockets and nukes and stuff, but even without those any serious threat to NK would come with devastating cost of civilian lives in South-Korea.
See e.g. [1], which estimates that "the DPRK could cause thousands of casualties in just a minute and more than 100,000 in an hour" and some of the case studies in that report have more than 200,000 in an hour. And all of that assumes only conventional HE rounds – no chemicals or nukes. And all of that is in the first hour alone: a full war would cost millions of lives (during the Korean war, South Korean casualties were about a million civilians and 250,000 soldiers).
You need to move carefully when you've got almost 6,000 pieces of artillery pointed at your head, never mind nukes, and the people in control of them seem rather unhinged.
I've seen people express this kind of "we should have just intervened" opinion before, and in principle I don't disagree, but it's really not that simple: both due to the strong risk of heavy civilian casualties, and the geopolitical impact with the USSR during the cold war (and to lesser degree, contemporary China and Russia – I can already see China invade Taiwan using "but you invaded NK!" as an excuse).
[1]: https://www.rand.org/pubs/research_reports/RRA619-1.html