The right thing to do is to strap the car seat into the airplane seat for which you paid for your child. Would you hold your child as a "lap baby" in your car?

Yes, it's an extra expense. Comes with being a parent. Sorry, but seeing people hold lap children astounds me about the risk they're taking. If there's any number of types of events (sudden aborted takeoff, heavy turbulence, etc.) those kids are going flying and not in the intended manner.

Car seats have been approved for use on airlines since the 1980s when my kids were in them. In my car and on the plane.