I'm sure they mean really well but this is a very dumb suggestion since safety for kids on airplanes is not an issue. The amount of children dying from turbulence or who could be saved in an accident is zero each year. Children are safer on planes than anywhere else, including in our living room.
If every single child on airplanes used a car seat we could possibly safe 1 (!) child every 10 years. This is according to research which FAA has done. During that time 400 000 people will die in traffic accidents. Tens of thousands of young children will die in traffic during this period of time.
The quote below sums up just how clueless they are about car seats. It shows very clearly that NTSB can't see the big picture and that they have no idea that safety on aircraft and vehicles can't be compared. The comparison is not applicable for many reasons.
If we are so careful to strap our children into car seats when we drive to the airport, then why are we not as diligent in securing them in a seat of their own on the aircraft?" NTSB Chairwoman Deborah Hersman says.
Nagging about car seats on planes cause more parents to use their car which means serious injuries and fatalities increase. The idea of making car seats mandatory would be a huge disaster since serious injuries and fatalities among young children would go up sharply instead since parents would use cars more often.
It will hopefully never happen but the aircraft/airline lobbying in US is very strong. More kids in car seats on planes means higher expenses for parents and billions more in revenue for airlines.