There are a couple of important things to consider. Most problem drinkers will sort things out on their own, this is well established fact. However Alcoholics of my type don't do so well. Of the group (of 10) I went through rehab with (if you could call it that) 3 of us joined AA and recovered. The other seven did not join AA and were dead inside a year. None recovered on their own. I do however mention that we were at the extreme end of the alcohol use disorder scale, suffering end stage alcoholism. This is a small group which AA seems best equipped to help.
On the subject of meetings, I have seen so many people drink over the years to know that meetings alone i.e. mindless passive attendance, does not keep alcoholics of my type sober. That is what the steps are for.
In the long term picture, meetings are a way to practice step 12, giving back to the still suffering alcoholic. That is the most effective way to stay sober. As someone else said, those active in service, and those sponsoring, seem much less likely to pick up.
The interest in meetings seems to come naturally as the result of the steps. I am not sure it can be a forced discipline. Sooner or later we would get tired of that. Most people I have been able to talk to who were thinking of leaving AA after a period, 2-3 years, of meetings based sobriety, tell me they want to leave because they feel they are getting nothing out of it. Nothing has really changed in their lives. Sometimes they change tack and get onto the steps, and then some change starts to happen.
To really guage the effect of meeting attendance on sobriety, one would have to check out why one is going to meetings, what one is doing there, and why one would want to quit.