We take our car seats on the plane for several reasons. First, though airlines may not require a toddler to have a car seat, the FAA recommends a car seat as the safest place on an airplane for children under 40 lbs. (rear facing if under 20 lbs.). The airplane seat belt is not intended for use on children under 40 lbs., and, despite airlines allowing it, a lap is not a safe place for a child to travel on an airplane (according to the FAA).
Second, after seeing what the luggage guys do to our other luggage (and having them break 2 strollers), there is no way I would check the seats. Assuming they arrive when you do (we all know luggage does not always arrive as planned, and you can't go anywhere without the car seat), I would not count on it arriving without damage. Aside from the damage that you might see, you have no idea what has happened to the inside of the car seat where you can't see it - there could be a crack in an important part of the seat, for example, rendering it unsafe. I really wish someone would sell a hard-sided case for car seats so we could check them through with confidence!
Finally, we find that the kids do great in their car seats on the plane. They are used to being in them in the car, and I think that helps them accept the restraint. It makes them feel more comfortable, IMO.
I won't lie - it's a pain to drag them around the airport. You have to put them through the x-ray machine at security and of course installing them in the plane is another hassle. My husband carries both car seats - one on each shoulder like backpacks. (I admit he is 6'4" which certainly helps - but you can get collapsible luggage carts if necessary.) Then he gets on the plane first, with the "people who need extra time" group. That way he can install the seats without backing up the aisles, and the kids can run around the gate area for a few extra minutes rather than sitting on the plane for the entire boarding process.
Just some food for thought!
