How Exactly Did "Al Qaeda in Iraq" Benefit from the Al-Askari Mosque Bombing?

Officially, "Al Qaeda in Iraq" was blamed for the attack.

Why would an Islamic group interested in uniting Muslims in a new Islamic caliphate want to do something as incredible divisive and heretical as bombing a mosque -- a place that was one of the holiest Shiite sites?

How on earth did this bombing further "Al Qaeda" goals?

On the other hand, the bombing did further the tacit goal of the US staying in Iraq long-term-- by creating sectarian violence that makes it difficult for the US to leave.

Obviously, "Al-CIA-duh in Iraq" makes more sense for the bombing.