Stanley Sloan makes the case:
Most would agree that the most vital American interest is defense of the homeland and protection of its citizens. An active alliance with America’s leading partners would seem to address that vital interest, even if the United States does not currently face threats of a truly existential nature. Having allies dedicated to considering an attack on one as an attack on all, as provided in the North Atlantic Treaty’s Article 5, is not a bad insurance policy – one on which the United States collected after 9/11....
The main strategic value of America’s European allies, however, is in the capabilities that the Europeans bring to the table, as they did in the case of Libya. Granted, European military resources have shrunk over the years, and the Libya “model” may or may not work for some other contingency. But as European allies reallocate resources as part of their withdrawal from Afghanistan, it is in the interest of the United States that they do so in ways that enhance their ability to assist the United States in dealing with future security challenges. NATO consultations can facilitate such an outcome.
I think Sloan was closer to the mark in the first graf: While it's difficult to see the U.S. entering into any conflict where it is the weaker power and thus actually in need of European help, a defensive alliance with mostly like-minded countries does provide something of an "insurance policy." In fact, as powers like China and Brazil pull more weight globally, having an alliance such as NATO ensures that the Euro-Atlantic region is firmly defended. It also makes economic sense for indebted Europe (and America) to leverage the alliance to achieve cost-savings in defense.
But this really isn't the case for NATO today, as Sloan makes clear. Rather, it's to have a set of allies to provide the U.S. with some additional capabilities (and legitimacy) for its international adventurism.
The insurance policy metaphor is apt. We would typically describe a person as insane if they deliberately hurt themselves just to luxuriate in the fact that they have medical insurance. By using the utterly unnecessary Libyan intervention as an example of NATO's worth, supporters of the alliance are chopping off their fingers, rushing to the ER and then waving the bandaged stumps around as proof of how important good medical coverage is.
To my mind, the case for NATO is actually closer to auto insurance - something that is important to have but that you try never to draw on unless something serious happens.