Well, the main answer to your question about "religion" (which I could turn into a debate about religion versus spirituality), is that the "spiritual experience" (or "spiritual awakening") IS what AA is about. It's what the first 100 alcoholics found worked for them when nothing else had.
So it's impossible, really, to talk about AA "minus the spiritual component." It would be a contradiction in terms. You wouldn't be talking about AA, you would be talking about something that adopts part of AA without the heart of it.
Anyone is free to create a recovery program that involves no concept of a Higher Power. Someone has--SMART, for example. There are others.
I don't know of any government programs in the U.S. that require AA any longer. The courts have held that it violates the Establishment Clause of the Constitution. Whether you agree with that interpretation or not, it's the law. Private organizations can require it or not. The government CAN, however, mandate alcohol treatment. Many people flock to AA for that purpose, simply because it is ubiquitous--it's free and it's easy to find. That isn't AA's doing, it's the lack of alternatives out there.