The point the OP is making is not about the justification used by the US Admin, but instead a point about how when a country has nuclear weapons, they are typically not invaded, because you risk those weapons being used. NK developed a weapon and has some degree of safety from direct invasion.
Since it developed nuclear weapons, Israel has never been invaded by a foreign country. Israel launched the 1967 war, and in 1973, Egypt only attacked occupied Egyptian territory. Same for Syria.
The fact that the 1973 war only occurred in Egyptian and Syrian territory actually had a major impact on how other other countries reacted to it.
Even the US - Israel's main backer - basically treated Egyptian and Syrian war aims as legitimate.
There is a widespread belief that Israel would have used nuclear weapons if the Syrians and Egyptians had broken through to Israeli territory, and that this was one of the major American motivations for resupplying the Israelis during the war.
