Oh no they didn't.
Wow no, they didn't.
They routed and ousted the "invincible" talibs/mujahideens from power, and gave the country to a different regime.
Here's what actually happened, Early 2002: The US and allies were feeling quite pleased with themselves, ready to call it as a war 'mission accomplished', if you'd asked any of the pro-American military analysts, they would have said that withdrawal was in sight, possibly between 2003/4.
Then what happened?
Come 2003/4, renewed insurgency, the taliban rise from the dead. In one of the greatest military comebacks in modern history.
And last I checked a great deal of Afghan land is classified as 'Taliban controlled' or 'contested control'.
Sure, the talibs can keep waging a guerilla war - but that doesn't mean that they were not routed from power in the first place.
The war isn't over that's the point, so how can one claim mission accomplished?
And they aren't gone, they are still there, they lose land, they gain, they die and somehow they come back. But they're still there.
After all, the coalition of the greatest powers achieved what they came to do, which was to dislodge the talibs from power and install a favourable regime.
No that's the easy part.
Tell me, would you call the Soviet effort in Afghanistan through to the Najibullah era a success?
Well, sure they installed a government dislodged all their political opponents, but in the end, we know who actually won.
As to how long they will want to keep that regime in power, how long they will be interested, that is a good point, but my guess is that it will be for a long time. They have a lot invested there, to simply let taliban come to power again in 2014.
True, I don't claim that they wont have interests but look at the scenario, growing discontent in the West about our involvement in far away lands, economic decline, strategically Afghanistan is of 0 interests to the US or Western Europe that was true in 2001, true now.
On the other hand you have an enemy that withstood unimaginable odds, and now the lone ANA with substantial backing is set to take them on.
And do not think that the end game lies around the corner, the talibs are a stubborn enemy, unless you defeat them 100%, the problem and war will remain.
The new democratic regime is there to stay, unless voted out by the people - which is the way it should be. US special forces, well trained ANA and USA's global reach can ensure that the talibs will not do more than keep waging geurilla war.
Ye know the US armed forces, NATO, ISAF and to an extent the ANA's war doctrine follows?
It is not the same way we do things like in Swat op, there's involves a lack of will to take the fight beyond their controlled territories, I see no scenario in which they are willing to end it.
For what it's worth, I cannot see the ANA winning on the ground, either the taliban win or a political settlement is reached (which I can tell you is very difficult, the issues don't just go back to 2001, but far far back).
Doing hit and run attacks is one thing, but winning territory is another.
Well, take a look at it this way.
American objectives in Afghanistan were to rid the land of the taliban and al qaeda, Mr Bush insisted initially 'we do not negotiate with terrorists'. New government installed, I agree on that it was a success but with some kinks such as the prevalence of war lords and drug lords in government and not a representative government which has a strategic effect. But today, the taliban are still around, and the al qaeda went from a few hundred in Afghanistan to many hundreds globally and the most dangerous of all, they went from an isolated fringe ideology to being integrated with others eg the taliban, as a result you have more radicalised people, suicide bombings for example are a product of this fact.
Now notice the U turn, they are negotiating with the taliban, somewhat desperately, they are negotiating, Obama came to his senses, calling it a 'hearts and minds' conflict, though his actions couldn't be farther from it.
The taliban went from seemingly complete defeat, and objective of survival, owning tiny fractions of land, those too being contested to as I said above: One of the greatest military comebacks in modern history, they are thriving some places, they have taken much land.
So how can you call this war a success?