To me, the concept of "couple privilege" has utility in the following way. Let's say that a unicorn hunting couple says they are seeking someone with whom to have a relationship, someone who will be an equal. We see this all the time. Generally, when you begin to delve into things, however, it becomes clear that this "equality" is no such thing, and yet the couple in question is having a very hard time seeing or understanding the ways in which they are not offering, and perhaps cannot offer, equality to their new partner. They are blind to the privileges that society grants them, and that they grant each other, as "the couple" as opposed to "the third". This can apply to people in preexisting couples who are starting new separate, vee-style relationships as well.
I know some people don't like him, but I really do, his writings have been of great help to me, and I found Veaux's take on it to me the clearest yet: http://tacit.livejournal.com/578925.html
Being in a couple isn't bad in the slightest, any more than being white or male is bad. None of these things should ever be thrown back at people as weapons. And none of these things have anything to do with the immense economic and social privileges we have as members of developed countries. But in all cases, it's valuable to understand the ways in which society treats one set of people differently from other people, so that we can better and more accurately respond to the context we're living in, rather than one we imagine. If that makes any sense.