Does the death of Osama Bin Laden mean the United States should speed up the drawdown of troops from Afghanistan?

Congressional leaders of both parties are saying it does, as are, reportedly, some advisers in certain quarters of the White House.

There are certainly legitimate arguments for winding down the war or altering the strategy. But they have little to do with the fact that the leader of al-Qaida is sleeping with the fishes.

First, as critics of the war have pointed out in different contexts, many Taliban factions have no connection with al-Qaida. If Bin Laden wasn’t running or even much inspiring the insurgents in his lifetime, his abrupt demise isn’t likely to grind the fighting to a halt. (Then again, if his diaries and thumb drives prove that he really was in charge of the Afghan Taliban, this calculation changes enormously.)

Second, those Taliban leaders who did have personal ties with Bin Laden—for example, Mullah Omar—may now have less reason to fight on. The possibility is at the very least worth probing. But it’s not at all clear that rubbing out the godfather makes his capos more amenable to reconciling with the Western-backed Afghan government. Some of Mullah Omar’s deputies or ground commanders might now find the notion more alluring. But officials say they’ve seen no spurt of defections in the 10 days since the raid on Abbottabad.

Third, the war in Afghanistan has never been entirely about killing or capturing Bin Laden. It’s a big deal that he’s been killed. Al-Qaida has lost not merely a figurehead but its political and spiritual leader, the seemingly invincible embodiment of its whole mythic narrative. But the organization and its dream aren’t dead; its franchise managers, however splintered and paranoid, can still wreak much damage. More to the point, Afghanistan, in its current state, would very likely tumble into anarchy or civil war without the binding presence (however tenuous) of U.S. and NATO troops—and thus serve, again, as a sanctuary for terrorists. Of particular concern here are the most-militant jihadists, who could turn the lawless terrain into a cross-border expanse from which to plan and execute their ambitions in nuclear-armed Pakistan.

This has been the real aim of the war, to the extent an aim has been articulated—to keep Afghanistan stable, at least to the point where the country can’t be taken over by forces intent on attacking others or fomenting upheaval in Pakistan. It’s maddening that Pakistan has done so little to quell this threat to its own survival. Or, to put it more precisely, it’s maddening that Pakistan’s military and intelligence services are split into factions, some of whose interests are aligned with the jihadists—and that Pakistan’s civilian government is too weak to root out those elements. But this is the trap in which we find ourselves.

The killing of Bin Laden would have momentous impact on the Afghan war—and on world politics—if some Pakistani leaders used the occasion to force systemic institutional reforms. Many countries’ leaders would be compelled to make vast changes if it were suddenly revealed that they’d been harboring the world’s most wanted mass murderer for five years—and that a foreign power can mount a military raid deep inside its borders without triggering the slightest detection, much less resistance. In just about any other country on earth, a leader would use this double embarrassment as an opportunity to clean house, chop heads, overhaul rival power networks.

But this is Pakistan, where the institutions suspected of harboring the mass murderer—and responsible for protecting borders—are in charge and in deep cahoots with the militant jihadists whose very existence jeopardizes the fate of the country. (For an enlightening history of this self-destructive symbiosis, see Pakistan: Between Mosque and Military, by Husain Haqqani. Interestingly, Haqqani wrote the book in 1995, when he was in exile at the Carnegie Endowment for International Peace in Washington, D.C. Now he is Pakistan’s ambassador to the United States and so spends much of his time trying, in effect, to convince our officials that his book’s thesis isn’t true.)

And so, the real potential “game-changer” of Bin Laden’s killing—that it might force the Pakistanis to break away from their darkest historical remnants and pursue a more civilized path—isn’t likely to happen.

This is the case not just because the military and the Islamists share the same power base, but also because the Taliban are a useful tool in Pakistan’s rivalry with India. Pakistanis view India as a much greater threat to their national survival than the Taliban or even al-Qaida. They continue to support certain elements of the Taliban—they want these elements to thrive in Afghanistan—in order to maintain a policy of “strategic depth” against what they see as their larger enemy. Should India invade (and there have been a few wars between the two countries since the 1947 partition), a friendly Afghanistan would be a strategic reserve. In the meantime, a strong Taliban helps counter India’s efforts to create a presence in Afghanistan—in other words, helps to pre-empt India’s encirclement of Pakistan.

The death of Osama Bin Laden doesn’t alter these factors.

However, domestic political pressures are building for President Barack Obama to speed up his plans to get out of Afghanistan. In December 2009, when Obama announced his plans to send in an extra 30,000 troops (on top of the 24,000 he added the previous March), he also said that he would begin to withdraw some of them by July 2011. (More recently, NATO announced that all troops would come out by the end of 2014.) With the magic date just two months away, the debate has begun over just how many U.S. troops—out of the current 100,000—Obama should withdraw and how many of those should be combat troops. Many are arguing that Obama should use the killing of Osama as an excuse (as Sen. George Aiken once proposed that President Lyndon Johnson do in the early years of the Vietnam War) to “declare victory and get out.”

It must be tempting. The war’s costs, in dollars and lives, are exorbitant. Despite the tactical victories that Gen. David Petraeus is racking up, the broader counterinsurgency strategy—which involves “winning hearts and minds” in order to get the Afghan people to support their government—doesn’t seem to be working, not least because the Afghan government is too corrupt or incompetent to earn their trust. (For the latest on this, see Jon Lee Anderson’s depressing report in the May 11 New Yorker.)

But if it matters to U.S. interests how the war ends—whither Afghanistan and its effects on the broader region—then it’s a bad idea simply to walk away. And it’s fairly clear that the outcome does matter to U.S. interests.

This doesn’t mean we should necessarily “stay the course.” We are getting out, if not in two months then (officially) in three years. All the players—the Afghan government, the Taliban, the Pakistanis, the Afghan people—are already behaving in anticipation of our departure. So we should, first of all, recognize that fact and make the most of it.

Afghan President Hamid Karzai must be extremely nervous that Obama will do what many in Congress, and some in the White House, are hoping—cite Bin Laden’s death as an excuse to go home. So we should exploit this situation, use it as leverage to get Karzai to step up reforms, especially to take meaningful steps toward ending corruption. As every U.S. leader has publicly stated, from Obama on down to Secretary of Defense Robert Gates and the entire military chain of command, even the most effective military campaign will have little effect if the Afghan people regard their government as illegitimate.

At the same time, commanders and diplomats should exploit whatever fissures Bin Laden’s death might have opened up—not just between the various Taliban factions but, more, between the insurgent commanders, who tend to lounge in the shelters of Pakistan, and the foot soldiers bleeding on the battlefields of Afghanistan. It’s unclear at this point whether a diplomatic settlement is possible, or what it would look like—but it’s time to start seriously crafting its foundations.

It’s also time for a serious diplomatic push outside Afghan borders. Early in his presidency, Obama recognized that this problem was regional in nature—and that the solution would have to be, too. The late Richard Holbrooke coined the term “AfPak,” to suggest its scope, but stopped short of AfPakInd, which captures things more fully. The leaders of India were the obstacle here, insisting that they be left out of any regional package, wanting to be dealt with individually, on their own terms, as the world’s largest, and one of its fastest-growing, democracies. They had a point, but it’s time to bunch the three countries together anyway, at least in a security forum, and perhaps to include Russia, China, and other interested parties as well. This is difficult, maybe close to impossible. But without dealing with this dimension, the problem won’t be solved.

Which brings us to the issue that Bin Laden’s death has revived as a debatable topic: the question of U.S. troops. The fact is that the United States needs leverage in order to apply the necessary pressure (to get Karzai moving on reform, the Pakistanis and Indians to get moving on détente, and the other regional and global powers to offer security guarantees, economic incentives, or whatever a peaceful arrangement requires)—and we will have no leverage if everyone thinks we’re getting out quickly.

It’s a delicate matter: holding out the possibility of a rapid pullout, to exert leverage on some fronts—while demonstrating a continued presence, and keeping up the military pressure, to exert leverage on other fronts. Maybe Obama’s new national-security team—especially Ryan Crocker, the incoming ambassador in Kabul—can juggle all these swords. Maybe it’s just not possible.

There are two alternatives to this approach: keep doing what we’ve been doing and stay there forever while the regional politics continue to stagnate—or just get out and watch it all crumble.

This is what the real debate should be about: what we want Afghanistan and its surroundings to look like in, say, five years—and how best to make that so. Anything else is a distracting cop-out.