Emotions don't belong in the workplace. They are there, but they too often don't help get things done. And yet, communicating is critical in order to both set expectations and to understand intent. Further, at least according to some references I've read, thinking diplomatically makes it possible to keep your emotions from interfering with your reasoning ability.
So if you're a manager or a leader, and you need people to work together that think poorly of each other, then you need a way to talk to them that won't amplify their negative emotions in the hope that you can maximize their ability to get stuff done. And if you are artful with it, you can have discussions about touchy subjects without getting dumped into an angry argument.
Poor leaders and managers use this to talk "over" people, generally young people who have yet to realize that conversations can have layers where what is being said on one layer is very different than the words that are coming out of the conversant's mouths. It is also popular to snipe at their fellow managers in this way.
That said, organizations that engage in a lot of "speaking in code" are often quite political, and that comes right from the top, the CEO. One of the great things about NetApp when I was there was that Dan Warmenhoven really didn't approve of that sort of crap and put a stop to it. At Google it was highly valued, and the politics reflected it[2].
An interesting warning flag is that if you are asked to say something (or hear something) that is a "bad thing" but clearly phrased in enough code to be deniable. An example would be "we need to move these employees into organizations that are more culturally compatible with the way they work." where the commonality of "these employees" is they are part of some protected class. Or "you need to get your team more focused on these deliverables" when team members have been speaking out about poor working conditions or, heaven forbid, labor actions.
At the end of the day, if a non-ambiguous statement would inflame emotions, it is going to interfere with getting stuff done. And in places where we are forced to work with people we might not normally choose not to associate with that means keeping things "diplomatic."
[1] Definition of Diplomacy: Telling someone to go to hell such that they look forward to the trip.
[2] I made a number of enemies in upper management by "translating" what they were saying into things that people could understand.