This was in the 90s though - what I still regard as the Golden Age of Flying (tm), and the Unaccompanied Minor service offered by most airlines was absolutely fantastic. You would be under constant supervision in the airports, get access to the nicer lounges.waiting areas, have priority for boarding/disembarking, and be generally treated like royalty.
Even if you were flying coach/economy.
It was totally brilliant, and I was heart-broken about losing this aspect of flying when I turned 16. (IIRC that's the age limit)
Come to think of it, the reason that UA screwed the pooch so badly on this could be because of the death of the Golden Age of Flying.
BTW, in Sweden the age limit for using this service is 12 - if you're 12 or older you're considered old enough to fly (again, domestic) alone, something my 11 year old daughter who turns 12 in a few months looks forward to as the last time she flew alone she felt that she was too big to've been "babysat" on the flight.