AA and NA are not only wholly unscientific, being invented of whole cloth by a layperson in the early 20th century (for context, lobotomy was a totally accepted psychological treatment for decades after 1935). There was no science whatsoever involved in AA, and indeed Alcoholics Anonymous actively resists any data collection about the efficacy of its techniques whatsoever.
It's main advantages from a US perspective are a) it's free. The costs are borne mostly in the form of churches providing basements and meeting rooms. and b) it's super churchy. We love churchy stuff around here.
So basically we kicked addiction under the rug for the entire 20th century in favor of religious hokum that refuses any objective evaluation of its efficacy, or changing its methods.
I should say, for the record, that there's a lot of people that have been helped by AA and NA, and there's indisputably good work being done there. But it's not perfect and categorically refuses to get better, and its longevity is IMHO more a result of our collective refusal to take the problem of addiction seriously in the US than anything else.