I wrote half a dozen very complicated answers to this question [academic-reflex behavior] but I've thrown them all away, because there is a simple answer.
The biggest problem in communication, across the board, is the failure to pay attention. Most of the time, we don't really want to pay attention to what other people are telling us. We want our own turn to talk. We want the other people to listen to us. We want them to hurry up and get to the point. We want to go do other things, things that interest us more. I once heard a truly miserable child say to his mother, "I wish I was dead," and heard her answer, "Were dead, dear. I wish I were dead." She wasn't listening; she wasn't paying any attention at all. We are such distracted listeners, and we so badly want to be listened to ourselves, that many of us are willing to pay professional listeners $100 an hour.
In any group of interacting human beings, the consistent use of Miller's Law helps people pay attention to one another's language; it helps them listen to one another and (if the communication is face to face) to observe one another's body language with great care. Anything that has that effect is going to make things better, across the board.
One of the seductive things about the very early stages of Romantic Love -- the "being in love" stage -- is the way you have that other person's full attention all the time when you're together. Suddenly, for perhaps the first time in your life, somebody is really listening, with interest. to every single word you say. That kind of rapt attention doesn't last, but it demonstrates that it is at least possible.
Miller's Law is a technique for paying attention even while (as a mediator, for example) you remain emotionally detached. It makes the people you're paying attention to feel respected and valued, even when they are aware that you disagree with them.