Here is a reason why AA incorporates a Higher Power:

First of all, alcohol to an alcoholic, beside dissolving fears, make them feel ten foot tall and bullet proof. They believe, while under the influence, that they are Einstein (even god), also the great romancer, and the great dancer, etc. A primary symptom of alcoholism are delusions of grandeur. This mental delusion of self gets them to think they can stop drinking whenever they want to, but they don't want to.

Recovery is the opposite to alcoholism. They have to quite playing god, because it did not work.
They can no longer rely on themselves when it comes to drinking alcohol. They have to rely on another power, greater than themselves.

Most alcoholics have been that way for many years. During that time they have unknowingly altered their thinking to support drinking.
There morals, ethics, rationality, judgement, discrimination, etc have been twisted to support drinking, but not sobriety.
When they stop drinking, they still have that twisted thinking. As some say, our best thinking often gets us drinking. An AA joke is: "If you take the alcohol out of a fruitcake you still got a fruitcake".
The tricky bit about being insane, is that you do not know your insane, because you are insane.

STEP 2. Came to believe that a Power greater than ourselves could restore us to sanity.

Recovering alcoholics need to rely on other than self. Most prefer God, as they understand God to be. Many say that GOD stands for Good Orderly Direction.

Secondly, the God concept works.