My experience was i worked the steps in the first few months of sobriety and basically the obsession for alcohol left and now a few years down the line i just don't drink, its no big deal and its a choice.
If i had cravings for alcohol i would drink, that's why AA worked for me i guess it promised that the mental obsession would go and it did.
Fortunately i don't really get the thinking a drink through thing. If the person has worked the steps to the best of their ability with rigorous honesty and still has the mental obsession then they are one of those unfortunates mentioned in the BB i guess? Dunno?