Can you give me an example? Because right now this ability looks like the tiger-repellent rock to me.
The United States vs the Soviet Union, for one. There are many examples, but a notable one was the secret communication that Chairman Khrushchev made to President Kennedy. It was a very long and emotional. While the two leaders were brash with each other in public speeches, privately Khrushchev begged Kennedy:
"It is thus that we, Soviet people, and, together with US, other peoples as well, understand the questions of war and peace. I can, in any case, firmly say this for the peoples of the Socialist countries, as well as for all progressive people who want peace, happiness, and friendship among peoples. [...] Consequently, if there is no intention to tighten that knot and thereby to doom the world to the catastrophe of thermonuclear war, then let us not only relax the forces pulling on the ends of the rope, let us take measures to untie that knot. We are ready for this. [...] There, Mr. President, are my thoughts, which, if you agreed with them, could put an end to that tense situation which is disturbing all peoples. These thoughts are dictated by a sincere desire to relieve the situation, to remove the threat of war." *
I think it's pretty certain that Krushchev and Kennedy being able to talk to each other helped diffuse a situation that brought the superpowers closest to the nuclear brink.
It was after the Cuban Missile Crisis that the Moscow Washington direct hotline was installed so that the leaders could communicated directly to resolve crises.