Captivep, if you can quantify how much this service actually costs BA and demonstrate that the money could be better used elsewhere in terms of, as you say, growing new business I would absolutely agree with you.
However if, as I suspect, the figures involved are absolute peanuts in the greater scheme of things then that argument ceases to be as relevant because all it is doing is deteriorating the public image and perception of the level of service that BA provide. That has repercussions way beyond the minute figures involved in maintaining an Unaccompanied Minor service.
Penny wise, pound foolish. It is seen again and again in this industry. The trouble is the Chief Execs concerned don't care about the long game they are there for short term gain, increase short term profits, collect their bonus and then move on to their next company. They could give a damn how the airline is doing in ten to twenty years time.