President Obama’s surprise visit to Afghanistan shows that he is determined to use the bin Laden killing to his political advantage. He also hopes to win points for ending two unpopular wars.

That is understandable. If nothing else, it allows him to draw distinctions between both his predecessor, who failed to find bin Laden, and the eventual GOP nominee, Mitt Romney, who argues against withdrawing U.S. troops from Afghanistan.

But the policy that President Obama is pursuing in Afghanistan is still at odds with what most Americans desire. The strategic partnership agreement signed by Obama and President Hamid Karzai embodies this policy. He chose to expand the U.S. presence in Afghanistan in 2009, and will now draw down to levels at or near those when he took office. That doesn’t go far enough: a majority of Americans want all U.S. troops out of Afghanistan within a year, and a large-scale military presence isn’t needed to continue to hunt al Qaeda. The organization is a shadow of its former self, and has shifted its operations and tactics to many other places. We are still spending tens of billions of dollars in a desperate nation-building mission; this money could be spent much more effectively elsewhere, including here in the United States.

Moreover, President Obama lacks the authority to make the promises that he has extended to the Afghan government and people. For example, he pledges to leave some unspecified number of troops in the country until well past the end of his second term (if there is a second term), but Congress determines funding for overseas military operations, including troop deployments, and there is no reason to believe that future Congresses (or future presidents) will feel bound by Barack Obama’s promises.

After 9/11, the American people rightly demanded that the U.S. government hunt down Osama bin Laden, and perhaps even to move heaven and earth to do it. It made sense to punish al Qaeda and degrade the organization’s ability to carry out another attack. Those tasks have been fulfilled. The mission of preventing the Taliban from rising again in Afghanistan is a hopelessly quixotic crusade, and one that we would be wise to abandon.