There has been an awful lot of "academic" skirmishes involving real live fire in that conflict over the years. Each one of these is playing a little with fire. Sometimes, things escalate for no rational reason.
No-one is going to start an actual war.
It's naïve to say "we were just trying to make the point X, we didn't think it would escalate" when the actors involved have the resources and incentive to react with interest.
If anything North Korea developing its own nuclear arsenal took war off the table. That was the point, although full-scale war was probably already off the table, but a more limited action to topple the regime probably wasn't.
It's borderline madness to suggest otherwise.
so far, MAD has kept that from happening again. But it's not borderline madness to observe something that definitely actually happened.
A war on the Korean peninsula already happened in the past and it went quite badly for all involved.
Now it is 2020, with very interconnected economies between all involved and with the US, China, Russia, and North Korea having nuclear arsenals. Therefore it is indeed borderline madness to suggest that anyone might decide to start a full out war on the Korean peninsula, it is even more ridiculous to suggest that this might happen "by accident" (like it is ridiculous to suggest that WWI started by accident).
In the real world of today one might look at Chinese-Indian relations. Probably 10s of soldiers on both sides died recently. Are the nukes flying yet? Of course not, no-one is suicidal and both sides won't attempt anything beyond their skirmishes in one or 2 remote valleys.
It's only sensationalist news channels that peddle the risk of war with North Korea.