My kids are a bit older now, but about 3 yrs ago (and earlier), an infant in lap was given a special seat belt which hooked onto the parent's belt.
I don't know if they still provide those belts. I haven't seen them on any of the US carriers.
It was a bit annoying to the child, but I felt a lot safer with Rawan jr secured this way, than wriggling around in my arms during turbulence (Having passed physics, I have a great deal of respect for the Newton's laws...)
When the infant had a seat (purchased or just happened to be empty), the FAs still asked that we use the infant restraint, while the seat belt sign was on. If we had a car seat, I'm sure that would have been acceptable too.
A good car seat is probably the superior form of child safety restraint. Having said that, I wouldn't buy one for one-way usage.
I hope I've answered OP's original question.