On April 1 this year, a riot erupted in Mazar-i-Sharif, the capital of northern Afghanistan’s Balkh province. Infuriated by a Florida preacher’s burning of a Quran, hundreds of Afghans overran a United Nations compound, killing three U.N. staffers and four security guards. The tragic incident was a reminder of how contemporary conflicts are increasingly shaped by a blurring of lines. A bigot on the fringes of American life becomes a player in a war zone on the other side of the world. Angry civilians become tools in the hands of anti-Western insurgents. And aid workers—devoted to improving desperate conditions in a war-torn country—become targets for deadly violence.

In a perverse way, the attack—and many others like it—mirror another blurring, one that has increasingly shaped American national-security policy in the past decade. An oversized but overstretched military is being asked to take on a wide range of responsibilities that have historically...

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