One of the best "weird" purchases we made was when DS1 was a baby we purchased one of those car seat covers/bags. It has a handy strap, if you want to carry it over your shoulder. It was something like $79 way back 11 years ago. Well, 11 years and three children and innumerable trips later its battered and scuffed but still GREAT! Without commenting on other people's choices, I personally think it's not safe for kids to travel on airplanes without car seats. So, we have and will bring one on the plane. What we do is put the seat in the carrier, toss in blankie and little pillow, and even the coats/jackets usually. We typically then put it on a rolling luggage rack.
I have never wanted to take the chance of having a child who either refused to sit with the seatbelt on or constantly opened and closed their belt, etc. I have one that would prob. have done fine, and two who would have caused us quite a bit of stress. Also, our car seats, and then our boosters all had 5 point harnesses. It is way too easy with even slight turbulance for a little one to be jarred around. With the 5 point I just feel they are more protected, even if the plane goes into a spin or flips over or violently on one side.
Finally, one time we visited WDW and DS got sick. The manager of the resort had a CM drive us over to a local urgent care and then to get meds! (Gotta love the pixie dust!) Anyway, I'd have really been in a bind if we didn't have the car seat. Another time we had to change planes in Salt Lake City for a trip and there was a problem with the plane and they put us up in hotels. Once again, had the car seat, so was able to transport DS okay. You just never know what could happen, I'd rather be safe than sorry.