Eric Alterman seems to hit on something that a lot of the rest of us have known for a while: not only is the United States unilateralist, but it doesn't even care what the rest of the world thinks. On some level, this isn't really surprising, and the explanation is fairly simple: the United States has enough power that it can do whatever it wishes. The problem, however, is not that what the United States is doing is wrong (international relations is not a field of rightness or wrongness, no matter what the current administration might believe) but that it carries long-term implications that I don't think the administration or even the intelligentsia have fully thought through.
If the United States cannot be dissuaded from doing anything, if it isn't even willing to listen to the views of what would appear to be its closest ideological and historical allies, then the perception will be that the United States cannot be trusted. If Europe believes that the United States cannot be trusted, then anybody that does listen to the Europeans on the topic will also come to that conclusion, even if the historical record showing the United States has an notoriously short memory internationally and has an exponentially higher interest in domestic politics than international relations hasn't already convinced them.
Sooner or later, the United States will need the assistance of other states in order to forward its economic, political, or military agenda, yet why in the world would any other state trust the U.S. any further than it could throw it? And what if Europe decides that it can't afford to live under the American umbrella, and decides to become a political, economic, and military rival to the United States rather than an ally? This is very unlikely to be the case right now or in the immediate future, but people aren't stupid outside of the United States, and unlike the U.S. the people and governments of Europe can have a long memory indeed of past slights. The world will not remain unipolar forever, and those who are stepped on by the United States while it's on top might not be willing to help it out if and when things change.
On a more practical level, it also means that the United States will have a harder time convincing other governments to engage in activities that really do have a collective benefit. Why lower trade barriers, for example, when you know the United States will just backslide? (There are valid economic reasons for still doing so, but we aren't talking about reason here). Why engage in collective diplomacy, nation building or humanitarian efforts if you think the U.S. will pull out whenever it becomes slightly possible that domestic interests may be hurt? Why agree to obey the myriad of international treaties that keep interstate travel, communication, and business civil when you can't trust the other guy to be reliable?
Yes, it does matter that the United States is ignoring Europe. It may not make a difference today, tomorrow, or next week; sooner or later, however, the perception of the United States will hurt it deeply, in a way that it couldn't have possibly predicted.