Let's imagine that all leaders got wiped out.
Other people would take their place immediately. Even if the entire chain of succession established in the United States were to be wiped out, someone would probably still step up, take the position, become the new "alpha" and then act abusively.
Even if everyone died except for the top 1% of "alpha" humans, they would still create social divisions. It's a part of human nature, although it used to be less extreme in times when humanity was more rural and even tribal.
They would all just be fucking with each other to the point of destruction because we wouldn't be there to complain or resist.
There are very few leaders I can think of who were irrational to the point of willing to risk complete destruction, let alone those who would be willing to risk it against the odds, let alone those who would do it with no chance of victory. Even Hirohito bent the knee to the Allies in time. Hitler did risk it against the odds, but if he took Moscow (and didn't declare war on Britain or the U.S.), he could have potentially had the advantage.
There are only three countries I can think of that completely shot themselves in the foot: Cambodia, Equatorial Guinea, and Rwanda. Even then, I suspect only Equatorial Guinea would be run by someone crazy enough to actually use nukes at random if they had them.