I'll apparently be in the minority here, but...
My smallish DS turned two a few days before we flew, and we did not do a carseat. Like you, we would have only needed it on the plane, and I didn't think it was worth the aggravation. We had no problem at all with him just sitting on the seat with the seatbelt on.
This was us too. My DD was tiny at 2 (about 21 lbs) but she fit in the seat just fine.
My concern is that in the case of severe turbulence, the lap belt is not going to restraint a petite two year old. Their little bodies have enough clearance to torque around the belt and - depending on the type of lurching the plane is doing - potentially hit the seat in front of them or the ceiling.
Obviously, on MOST flights, this is not going to be a problem. What I commonly hear from parents, though is, "Well, if the plane comes down, we're all dead, so why should I bother?" And, certainly, I can see that. But there are unforseen events - air pockets, turbulence, etc - where adults will be just fine, in their adult-sized seats and lapbelts. But a babe in arms or a toddler will not be kept safe in adult-sized restraints, and that is where a child restraint could be invaluable.
Again, most likely, not a problem. Then again, most of us could go 98% of our adult lives never buckling up, and we could be fine. It's that remaining small percentage - which, unfortunately, we don't know ahead of time is coming - that we have to be safe for, the rest of the time. Since the OP's original question was how to safely transport her child, the answer is to use a carseat. If the answer is how to do it easily and conveniently, then of course, just sitting the child on the seat makes life better.
I have seen some really creative setups for parents to get onto planes. Example: carseat attached to rolling luggage cart. Backpack or small duffel of toys and snacks in the carseat, strapped in with the (loosened out) harness. Child can walk ahead of the parent or ride in a baby carrier. Or ride in the carseat, with backpack of toys on the parent's back. Etc...
I am, unfortunately, the product of too many case studies, reading too many crash articles, etc, etc. There are a million, billion risks that we take on a day to day basis with our kids (like putting them in cars at all.) Everyone needs to decide for themselves where their risk tolerance lies. I personally cannot take the risk - especially when it is as simple as carrying a safety device that I already own onto an airplane. Part of the reason I do what I do, in terms of working in injury prevention, is to share with other parents all of the stuff I did wrong because I didn't know better. So I am dedicated to saying to parents, "Hey, there is a safer way to do this." Whether or not parents choose to listen is up to them, but at least they have been presented with the information. When you know better you do better, right?