Sufism is version of Islam that promotes peace and a universal connection to God. It is very common in history for invading armies to try to convert the countries they invade to new religions that better suit the political goals of the invaders. This isn't necessarily a bad thing. In the case of Sufism, it is already a version of Islam, so the resident populations of Iraq and Afghanistan would already be familiar with the basic concepts. The main advantage of promoting Sufism is that it would unite all of the people in Iraq and Afghanistan into one brotherhood of peace rather than the variety of factions that are now battling for control in those countries. Everyone would be working toward the same goal, which would be a peaceful society of mutual friendship where everyone goes to the same church.
Putting one group in charge would definitely lead to a more rapid stabilization, but it would in part be defeating the purpose of the wars in the first place. It would also make it look like the US was playing favorites, which would lead to futher problems down the road.
We could not have tried to promote one sect of Islam over another in our invasions of Iraq and Afghanistan. Those people had been set in their ways for centuries and would not have changed. Our support would have made change even less likely as many there feel that we are anti-Muslim.
No, the wars in Iraq and Afghanistan could not be ended sooner if the invading nations were to promote Sufism and assist Sufi teachers, because the United States cannot come in and impose a religion or belief system on the peoples in those countries. The people have to find peace within the confines of their own religion.
I think that the issues in Iraq and Afghanistan war are very complex and something like promoting Sufism would have little effect on the overall progress of the war. I think the wars are primarily focused around combating militant groups that are terrorizing military bases and cities and those people would not let up even if the invading nations were promoting Sufism.