I'm not sure what the statistics are on car seat safety and airplanes. And yes it can be a hassle to lug them around. However, if you buy a separate ticket for you child so he/she has a seat, the seatbelt is like the seatbelt in a car. It's not calibrated for such a small body.
Most airlines let you take kids under a certain age (2 I think) as lap babies, meaning they have to sit on your lap if you don't pay for a seat. Personally, if I pay for a seat, I would take the car seat. Worse case scenario, I'd rather have my child crashing in a car seat than in a plane seat. Just seems safer to me.
Car rental companies will rent kid seats to you. I don't know of any that include them for free.
wouldn't you just love to beeeeeeeeeee me? "-)