I don't even know if it's really about cost either. There has to be some other reason for this.

Most minors who would have elite status would be travelling with parents who could guest them in anyway, so I think the amount of lone minor travellers clogging up lounges would be pretty small, except for perhaps LHR where many kids attend boarding school.

Besides, I think the cost of food/drinks consumed in the lounge can't be too costly. After the first few times where I used to get excited about lounge food, it's now more of a place to relax and grab a coke or small snack before flying. In fact, often at HKIA I skip going to the lounge entirely and prefer to grab a meal at Pizza Express and then just sleep through the flight.

I guess we'll never truly know why the policy exists. I could understand if they didn't want under 12 to have it because they pay lower fares, but for people paying adult fare, they shouldn't be discriminated against.