If by "launching a nuclear missle" Elon means NK using a missle to target and explode a nuclear warhead in SK, Japan, or a US territory, then of course there would be a massive armed response and NK would cease to exist. But I doubt very much that NK would do that. They will continue to do things that are not direct attacks but that demonstrate their growing capabilities.
NK wants the US to negotiate a peace treaty with them directly. We have no choice but to do that, as the alternatives all involve hundreds of thousands or even millions of people dying. Such a treaty should not include letting NK take over SK. But we could recognize NK and possibly negotiate an end to hostilities. It has to be attempted.
Anyone who makes the decision to attack NK now, before NK has attacked (launching missles over Japan is not an "attack") will go down in history as a mass murderer. Some people apparently think that attacking now is preferable to allowing NK to have long range missles armed with nuclear weapons. I don't agree.
The real question is what does Kim#3 want?
I suspect that there are a lot of internal political machinations that we have no clue about. As
@mrElbe pointed out, there may be old guard support for Kim#3. Survivors of the Korean War, they would have only one desire--unification under NKorea and punishment of their enemies--mainly Japan and US.
Obviously I cannot see in their brains, but you see a lot of older Chinese who have similar desires and pent up hatred, and one can see their comments on line (or translated comments at least)--very supportive of their traditional allies in NKorea. We all have to understand that a lot of the old guard see China's market moves as a complete violation of the original founding of the People's Republic. Hence why Xi is moving China toward Confucianism, using that principle to give legitimacy to the Communist government.
Are we all willing to sell SKorea and Japan out like that?
As for what the younger generation want, maybe lifting of embargoes and free access to trade. That may be achievable, but if Kim#3 is of the old Guard faction, then that may be irrelevant. The whole concept of self-sufficiency and self-reliance coming to play here (Junce-sp?). No need to trade if you're an autarky and have everything you need (not necessarily want).
Further, would Kim#3 really want to give his people a better standard of living? His army yes, his people I'm not sure. This falls back to the inverted J-curve of history. Once the people start to see a better standard of living, they will expect more. Once those "more" stop coming (and the curve starts to go down), that's when governments get overthrown. Then again there was an episode early in his rule where he tried to impose currency controls to curb the black market, that ended VERY quickly, so the NKorean people do have a "vote" so to speak somewhere.
The key for him is to unify the army under him (IMHO). As long as he can get hard currency and food and oil for his army he's ok. IMHO, that's the whole point of the demonstrations of their missile capability, to impress his army with his resolve and defiance of all enemies. Trump yelling at him helps his cause, btw.
It seems to me, he really is the King Joffrey of NKorea. IIRC his interests in boarding school in Switzerland were Pornography and Dennis Rodman. And the methods he has used to kill his internal enemies have been just as ruthless--and intended to terrify his hidden enemies.
So what to negotiate? I don't know.
Either way, I really think all this missile firing is a show for his army and "people". I am hoping that is what it is really about, and this will blow over once he cements his own power in government.