Seoul is close enough to the DMZ to be in the firing range of conventional artillery. There's a non-nuclear form of MAD at play.

DPRK is useful because it can inflict damage and threats without having its masters (most likely Russia or China) getting directly involved.

Also helpful to collect intelligence.

Sending missiles toward Japan directly hurts the economy of Japan and its political stability (which in returns, has positive effects that the competitors of Japan can reap).

A buffer State. The PRC doesn’t want the Korean Peninsula used as a land-based route for an invasion of China by Japan, the US or Russia. Even if the DPRK is a problem, it’s also a barrier to entry for invading China and that’s good enough for the PRC to still support it.

> I guess there is still the concern that China would back NK, but I can't see what China benefits from that. A war with other superpowers to protect a poor, weak, unpredictable regime?

North Korea has been very useful to China. You could make either case: that China would come to NK's rescue [1], or that it would hasten its demise [2].

There is also the possibility that North Korea would nuke Beijing if it was on the brink of defeat and China didn't come to its aid. The distance between North Korea and Beijing is only a few hundred kilometers, after all, and though North Korea may not have China's sophisticated arsenal of missiles, it has enough functional short range and medium range ballistic missiles to wipe Beijing off the map. A kind of reverse NATO, if you will. China might be condemned to back North Korea, even if it doesn't want to, under threat of nuclear annihilation.

[1] https://www.foreignaffairs.com/articles/north-korea/2022-02-...

[2] https://www.foreignaffairs.com/articles/asia/2017-12-12/why-...

North Korea has nuclear weapons. They have ICBMs that can hit west coast of US but few enough that maybe could be intercepted. They also have shorter range missiles that threaten South Korea and Japan.

North Korea has few enough nukes that first strike to take them out is possible. But would likely require using nukes. China, and much of the world, would not be happy. Acceptable if war has broken out, not to start a war.