Did you laugh at Slim Pickens in Dr. Strangelove? The joke's on you
Did you laugh at Slim Pickens's antics? Did you think it was funny that such a gung-ho idiot would be trusted to protect us from the Soviets? Well the joke's on you - he's the straight man in this movie.
In Dr. Strangelove, almost all of the "higher ups" act like super-intelligent protectors of the American people, but they are all too juvenile to focus on their jobs. When the commanding officers and Strangelove aren't quoting Georges Clemenceau and Herman Kahn, they are busy measuring their dicks and trying to get laid. The Russian diplomat wastes valuable time bickering about food and taking pictures of maps in the war room, and USSR Premier Kissoff is drunk and hysterical through the entire ordeal. Group Captain Mandrake cowers and grovels when Ripper (an officer who outranks him) threatens him with a gun, but when a lower soldier who he obviously sees as a grunt point a gun at him, he bosses him around like a child, despite the fact that Ripper is the one who is actually deliberately starting nuclear war and needs to be stopped and the soldier is actually on Mandrake's side. The soldier in turn can't put 2 and 2 together, and concludes that Mandrake is a "prevert" and decides to protect Coca-Cola's property from him.
The only character on the ground who seems to be the level-headed voice in the room is President Muffley, but he is shown pretty clearly to be in over his head. He spends most of his time reprimanding and reassuring the crazy people around him, calmly talking to the Premier about how "it's good to be fine" and separating Desatzki from Turgidson from their petty fights with his famous "there's no fighting in here, this is a war room" line. And in the end, in his efforts to mediate and manage the personalities, he makes the error that decides the fate of the world - he tells Premier Kissoff to "throw everything you've got" at the 2 targets of Kong's B-52, not considering the possibility of what ends up happening - that the plane can't make it to its original targets and diverts to a different one which is completely undefended.
Kong is a stark contrast to all of this. While he doesn't come off as a smart guy who is deserving of his role protecting his country, he actually possesses valuable qualities that help him focus on his job. When they got the order to execute "Plan R," he made the radio operator ask for a confirmation and checked the transmission himself. He then did something no one else does in this movie - recognize that people have differing opinions and that feelings might cloud people's judgment with his line "y'all wouldn't be human if you didn't have some strong personal feelings about nucl'r combat." This would have been valuable advice to give to, say, the Soviets who decided to create an automatically triggered apocalyptic weapon, Ripper, who decided that his sexual performance was a Communist conspiracy that must be countered with total annihilation, or Turgedson, who assumed that the Russians made the doomsday device up to trick the US. Even through extreme danger, Kong keeps his cool and gives his mission a change to succeed, even at the expense of his own life. The real irony of this movie is that the one character who knows how to to his job and stay focused isn't able to communicate with the idiots commanding him.