I have personally seen what can happen to bags and how travel strollers, pushchairs etc can be thrown around carelessly by airport baggage handlers. My father used to see it all the time as an aircraft engineer too.
Whilst your car seat is likely covered by your travel insurance, it can take time organising a replacement which could restrict your movements and plans. Using a car seat bag can mean you can store some extra items to help pad it out, like diapers/nappies, a cuddly toy etc. (This way, you get a little bit of extra baggage, but shhhh, keep that quiet!)