As a parent who has traveled with a child and brought a seat, I must say, the airlines do everything in their power to discourage their use.
Car seats, especially once the child is over 20lbs, are bulky and difficult to transport. Moving through the airport was not an issue, they make a strap that hooks them to a roller bag. However, once at the gate, we were only given priority boarding once, meaning I had to navigate down the isle with this bulky item trying not to hit people already seated. In order for the seat to fit as designed, I had to recline the chair all the way, which i am sure was none too pleasing for the passenger behind us. The seat barley fit between the two rows necessitating it be placed next to the window or it would trap the person on the inside, unless they wanted to crawl on the floor. There is no clearance next to the window making it very difficult to get the seat strapped down securely. If I flipped the seat around, front facing, then I still needed to have the seat reclined fully but then it meant the person in front would also have been kicked the entire flight, which I am sure they would have not enjoyed.
So, while I bought a seat, brought an FAA approved device trying to one protect my child and to also be less onf an inconvenience to others around us, it turned out to be the opposite. She had to sit with her knees bent in the seat, regardless of position, so about an hour into the flight, she wanted out. Wouldn't you? The seat in front of her was not able to be reclined and her seat had to stay reclined the entire flight. She was perfectly calm, quiet and pleasant the entire flight, but the seat was a huge pain!
Rant off.