For some time before them, national "leaders" felt immunized against the personal consequences of war. The H-Bomb and the intercontinental delivery system ruined that for them; they can no longer be certain of surviving an all-out war. Deep bunkers provide only superficial reassurance, as there's no theoretical upper limit to how large an H-Bomb can be. If detonated at ground level, the Soviets' 50 Megaton "Tsar Bomba" could destroy any bunker in existence. Larger H-Bombs can be built without straining the physics involved. If any such superbombs exist, they're a closely guarded secret.Tsar Bomba was originally designed to yield 100 megatons, but the Soviets de-rated it to 56 megatons because they were afraid of what 100 megatons might do.
Edward Teller said that once you got a bomb to a certain size it merely ejected a puff of Earth's atmosphere into space. The bigger the bomb, from that point, the faster the puff would go.
Thermonuclear bombs are multistage weapons. They have a fission bomb that provides the necessary kick to start the fusion reaction, but once you get the fusion section started, it will continue as long as it has fuel. That's what "no theoretical upper limit to how large an H-Bomb can be" means; I suppose at some point you will run into a problem with physically containing the fuel long enough for it all to be used, but that's obviously somewhere far north of 100 megatons' yield.
(In his various novels, H. Beam Piper talked about a strategic weapon he called a Hellburner, which was a bomb that generated a sustained thermonuclear reaction that lasted minutes or hours rather than nanoseconds. Only defense: stay away.)
Nuclear weapons have made total war strategically impossible. Let's imagine a fight like the European front in WW2, only somehow nazi Germany figured out how to build crude single-stage fission bombs soon enough that the first one was ready for use in December of that year, and it would be able to build approximately one per month for six months under the conditions they were then in.
One fission bomb at the Ardennes would have blown a huge hole in the Allied lines there. One more fission bomb in the right spot would have been a serious blow against the Soviets. I don't doubt that the nazis could have found a way to deliver such a bomb to Moscow, even if it was a one-way flight. (The V2 could never have carried one, though, as the payload of a V2 is about 20% of the weight of the first nuclear bombs. But a V2 could carry three W80 nuclear warheads, each yielding up to 150 kilotons. Fortunately, this hypothetical situation is not a time-travel story.)
And you will notice that the instant we had nuclear weapons, the instant their true power was demonstrated for the world to see, that was when total war ended.
The results of a full exchange between two nuclear-capable countries are terrible to contemplate. The bombs themselves can only ever be considered strategic weapons, because they're expensive to manufacture and their effects are difficult to contain. You won't use a nuclear bomb to take out a factory complex in the middle of a major city. There's no such thing as a "tactical" use of a nuclear bomb, because as soon as one side pops one off the other side retaliates, and pretty soon you're at "full exchange".
And so, yes: the advent of high-altitude precision bombing, and then intercontinental ballistic missiles, makes a defense against nuclear weapons virtually impossible. That means that the high-and-mighty, who were once insulated from war (except in the most dire of circumstances) were now just as exposed as the poor dogface out on the front line. And in our case, that was true for both sides: the old shitheads in the Politburo were in just as much danger as the old shitheads in Congress. If war began, it wasn't just the lives of a few million sons of peasants or rednecks on the line--disposable proles--but the lives of the leaders themselves.
This exerted a huge downward pressure on the declarations of war.
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Before the 20th century, even if you were a king (sometimes "especially if") your sons joined the military. Military service was expected of anyone who might be king, because someday he'd have to make decisions about using his army. The future king needed that experience. But this also provided a stopgap, because it kept the king from declaring useless or spurious wars. He would tend not to risk his heirs in pointless fights.
Of course, in 20th century America, the elites found ways around that: simply put them in places where they won't get hurt. Lots of future Presidents served in the reserve forces. That doesn't mean that none of them faced combat--several did--but by and large the scions of important families didn't have to worry about getting killed in combat.
Ending the draft, though, keeps those scions out of the military. It's all volunteer now, and the rich and powerful don't volunteer. Further, there's no societal pressure for them to serve, thanks to how Vietnam went. And so we now have a situation where politicians feel free to use our military to stick our noses into shit all over the world which has absolutely nothing whatsoever to do with us.
But you will notice that it's never against nuclear-armed countries.