Out of this whole conversation, I think the part that bothered me the most was the tradition of inducting an active parent with their child.
Ok, as a youth, I was elected by my peers for membership. Is it really different for Adults? Or is this just a fancy way of electioneering to induct the parent?
That said, I've had a love-hate relationship with the OA my whole Scout career.
As a Youth, I was honestly surprised to be elected, and honored to join. We did a lot of off-season service projects to help improve and fix up the summer camp. My Troop actually never went to our Council camp, so I joined the OA lodge for the nearby Council whose camp we did go to.
My co-ed explorer post didn't particpate with OA because at the time (maybe still, I'm not really sure), the female youth members were not eligible.
As the Summer Camp's program director, I was frustrated that, during camp, the local OA (youth) leadership, could never muster enough participation to even complete a Scout Law trail (a tradition for the closing Campfire was a trail walk where every 20-30 yards was a plaque or post for a point of the scout law and an arrowman reading the full definition of that point by candle light over and over as the campers waled past.), much less in-camp service projects. Sometimes, they couldn't even muster an election and/or induction team for those units that qualified. They were able to stage a dance team (sorry, I forget the exact term) event.
As an adult cub leader - the OA has been very helpful in our arrow of light ceremonies each year.
As an adult Scouter, I've honestly had too many other things going on to attend the chapter meetings - which until recently were at the same time as Roundtable. I have seen them supporting some of the District run events and parts of the Scouting for Food drive that we do. Also, as an adult, I think I would feel almost out of place just hanging out with the Youth OA members, and I already have too many Scout jobs to take on Advisor responsibilities as well.
As for purpose, I had always understood that Service was their big claim, but in practice, it seems intended as a way to keep some of the older boys involved in Scouting. In theory, they are supposed to reamin active with their Troops, but I have seen some get so involved in OA stuff, that they really didn't participate much with the Troop, so that's harder to see in practice.