The AA Big Book says nothing about being "powerless over your addiction," as you wrote. The entire program is based on the powerful reality that we can, indeed, do something about our "addiction." Nor does the AA Big Book mention anything about how to stop drinking, what you describe as a "symptom." Though it may not work for everyone, AA's program of recovery treats the whole person, the person we "learned" to become -- and who, in fact, we became -- while we were drinking. Did you have any power or control over the person you became or what you did or didn't do while you were drinking? Is that the person who you intended to become?
If what you do while you're drinking is what you intended to do before you started drinking, then you're not powerless over alcohol. But if what you do while you're drinking is beyond you're control to change or modify it in any meaningful way, then "something else" is in control.
Overcomplicating or misrepresenting a simple idea is both misleading and utterly unhelpful. This goes for people who've gotten sober in AA and those who have not.