Nukes make individual countries safer, but every additional country with nukes makes the world as a whole less safe.
I think a part of the reason North Korea plays crazy is because they have to. If the US didn't think they'd push the big red button, then we'd invade them in a heart-beat. Mutually assured destruction only works when you believe the other guy will push the button. So you need the bomb and then you also need to make sure everybody thinks you're willing to actually use it.
North Korea has enough conventional rocket artillery within range of Seoul to level the city. This is how Kim was able to run his nuclear program to completion in the first place. It also hasn't changed.