The American Academic of Pediatrics released a statement in 2001 supporting the mandatory use of Car Seats for infants on airplanes. Aaron Carroll writing for The Incidental Economist explained why that would be a very bad idea:

• Such a policy is estimated to prevent 0.4 infant fatalities per year
• But the cost of an extra airplane seat for infants (currently parents are allowed to carry them on their laps) would encourage more people to drive instead of fly. Since driving is more dangerous than flying a policy of Car Seats on airplanes would increase the number of child deaths by 5-10%.
• Overall requiring Car Seats on airplanes would cost $1.3 billion per life saved.

To read more about the implications of such a policy, and some better (and significantly cheaper) ideas about how to prevent child deaths, read the full argument here.

Source: The Incidental Economist