Technically, a child can sit in the lap belt after their 2nd birthday, when they have to occupy a seat.
This is not the safest option but I had to do it because I was flying alone with three children on transatlantics and I could only handle one car seat. If the CARES harness had been available, I would have used that. We kept car seats, and now boosters at my mom's so we didn't need to take them.
It's not just turbulence but take-off and landing. The child is simply not as secure.
Also, I've flown European companies which didn't allow my car seats on board. Yes, they were less settled and there was more jumping around.
The question is really, do you need your car seat on the other end? That would be my deciding factor.
NEVER CHECK A CAR SEAT IN AS LUGGAGE!!! Don't risk arriving at your destination, only to find that your car seat has gone somewhere else, or have your car seat show up in bad shape. Scary that it could be damaged and it wouldn't be obvious.
While airplane crashes are rare, lost and damaged luggage happens all the time.
I also just took our seat, a Radian, on our last flight, last week. My dd is 5 1/2. The FAA now allows approved restraints up to age 18 (covers handicapped) so it's allowed on U.S. companies. A three year old has to have a seat so they crew cannot refuse the car seat.
I rolled the Radian on a metal luggage cart and it was no problem. We did have some airstairs and had to take a bus at Frankfurt Airport (better than sitting on the runway for 2 hours like before) but I just waited until the majority were off and tucked it under my arm. My son took the luggage cart.
That was probably our last flight with a car seat, which marks 10 years of flying with them. It's not a problem but I only bring on board what I need for the flight, even if it means paying for checked bags.