Perhaps the reason AA has such a high initial dropout rate is that people realize that it is just a front for the Bible thumpers.
Except it isn't. People who make AA/NA work for them understand the need to move beyond the literal imagery of the steps and find a way to look at them that helps them - even if it means replacing references to "god" with some other image that works for them.
I realize you have a big hate on for anything that smells like religion but you should not let your irrational prejudices cloud your judgement. Remember that addiction is a fundamentally an irrational problem and if using god/spirituality allows an addict to manage their obsessions then why is that a concern?
As far as the drop rate goes: what is the drop out rate for your unnamed "modern treatments"? My bet is they have manipulated their stats to avoid counting drop outs.