^^ One way I discuss the "God thing" (and wording, and use of the Lord's prayer) is when and by whom the BB was written (and AA formed). White men in the mid-20th century with the common Judeo-Christian ethos of our country. (Here, you can also delve into the Oxford Group) Many lay people, authors, and sure, religious leaders have used God (or their word for a specific HP, like Allah) in writings and teachings.
"Modernize" that language- and, even specifically use what the BB says if you read in full "God of your understanding." IMO it's semantics, a reason "not to do AA," etc- basically, as was said above - to keep drinking. Also IMO - there has to be "some" word in a prayer- and the Lord's Prayer is so common that to me it makes sense it was a go-to given the time/place/whom of the BB.