Ever since the cold war, the United States will only go to war with a country that doesn't have the military or nuclear capacity to return the fire.
Didn't we go to war with Iraq over "weapons of mass destruction"?
Consequently, peace and diplomacy would be used more often under that fear of the alternative-getting bombed.
You make the assumption that half of these countries would react to problems reasonably while in the possession of nuclear bombs.
There's a reason everyone pisses themselves whenever news about North Korea or Iran developing nuclear weapons hits the news. We can't trust these countries, and obviously we shouldn't give them nuclear weapons.
