If you sit and really think about what a booster seat's function is, you'll realize that booster seat on an airliner is completely useless.
In a car, very short people, such as children, can be injured by the car's SHOULDER belt (the one that goes diagonally across and down from the shoulder to the hip). A short person will have the shoulder belt going across the neck or face, a VERY dangerous situation in a collision. All a booster seat does is raise the child up so that the SHOULDER BELT will be a life-saver rather than a life-taker.
In an airliner, the only seat belt is the lap belt. There's no safety concern about a child being too low to safely wear a lap belt, and there's no safety advantage to the child being higher off the seat.
I hope this helps explain why booster seats are not at all helpful on an airliner.