This stinks.
I really wish they would vary the fee based on number of flights. I can see charging a higher fee if you are making a connection and the airline is responsible for getting you from one plane to another , but if the UM is flying one leg with a parent / guardian at each end, $150 seems a bit excessive.
It really should be something like $50 for each leg, plus $50 for an escorted connection.
My 12 Y.O. flew last year by herself PHL - ORD. Rather than pay the UM fee ($165), I paid a little over $100 to upgrade her to first class. This gave her a single seat on a CR7 so she wouldn't have to sit by a stranger, plus I knew the FA up front would pay a little more attention to her. I was allowed through security at PHL to accompany her to to gate, and my wife was allowed through security at ORD to pick her up.