I still haven't read the article but I can't resist to react.

I do not think it did prevent WWIII, since (and I assume you are talking about the cold war, USA vs USSR) the USSR had no plans for an invasion and neither had the USA.
The thing is with an air strike is that you do not know if it's a nuclear bomb. If certain states would get such a bomb and launch a missile on their opponent, that opponent might think it's a nuclear bomb and react with their own.
Also the more countries have such a bomb (especially if they are corrupt) the easier it is for certain groups to get one as well and do some terrorist attack with it. 'Normal' terrorist attacks are already horrible but if those people would get their hands on a nuclear weapon it would be devastating.
Furthermore where people are mistakes are made. The more bombs in more countries the more likely someone makes a mistake.
If a war would happen in the end (and history tends to repeat itselves) it would be a nuclear war, if every country had their bomb, and this would mean the end of the world (atleast for us human beings as we are now). How awful it is a WWIII is not the end of the world. WWI and WWII already did prove that.
And last, would you want to live in a society based on fear? Conflicts between countries would be solved based on the nuclear bombs. In the end that would give only a few results. Countries would, out of fear, stop diplomacy and become isolated. Or conflicts would never change since others can't exert influence since the other has a bomb anyway. Or they start throwing bombs on eachother. Or the the only positive result would come forward: 1 country for the whole world. All people under one government. But then again nuclear bombs wouldn't be needed anymore since there is only one country. And this goes against the idea of each country their own bombs...