The costs of the Iraq and "Afpak" wars will break us. What the Bush and Obama administration's insistence on having a huge military reaction to the 9/11 attacks will do is to establish Osama bin Laden in the history books as the most brilliantly successful terrorist strategist of all time. He must have realized from the start that the knee-jerk militarists in our society would be our downfall.
Was the core purpose of the Afghan war to prevent Al Qaeda from having bases in Afghanistan?
As a terrorist, not military, organization, Al Qaeda never had great need for easily detected military style training bases with obstacle courses, rifle ranges and such. Their actual terror work gets done in apartments and garages -- often located conveniently in the target country. The main use for military style bases has been for making propaganda videos. Recruits need something more visually inspiring than conspirators sitting around a kitchen table going over maps and photographs. If Al Qaeda lacks bases of this kind it is a loss but only a minor one. To the extent that military training of recruits is actually useful, Al Qaeda will get hundreds, even thousands, of recruits well trained by the US and NATO as they desert from the Afghan army. Many of these deserters will have already been Al Qaeda recruits when they enlisted having been driven to Al Qaeda by occupation offensive actions, especially civilian killing air strikes.
A repeat of anything like the spectacular 9/11 attacks are unlikely now with law enforcement and intelligence agencies on alert for them. The most likely source of terror attacks at home now are US citizens or residents with religious or ethnic or family connections to victims of the Afghanistan invasion and occupation. Would be terrorists with such connections coming from Asia or the Middle East would be watched or denied entry.
So is the answer to add troops for counter-insurgency "clear and hold" and training of Afghan forces? The more added troops the more combat operations and training missions. The more combat operations the more recruits for the Taliban and Al Qaeda, The more training of Afghan government forces the more trained defectors to the enemy.
To sum up, the benefits of the Afghan, (widening into "AfPak"), war to Al Qaeda are (1) the US and NATO provides military training and even equipment, via Afghan army deserters, to (2) the new recruits created by combat operations causing collateral damage in an Islamic, tribal and insular country and (3) troops and civilians in the US or Europe which are out of range for Jihadi enemies in Asia are sent to Afghanistan by the tens of thousands where thay can be picked off by illiterate tribemen with grudges -- all this at great expense to the West but no expense to Al Qaeda or the Taliban. If history somehow fails to award bin Laden some kind of terrorist brilliancy prize then it can only be on the grounds that his success was really due to extreme stupidity on our side.