The math is more that benefits aren't that great and the dangers are pretty big, especially if someone fails to properly secure the carrier and you get a rejected takeoff
This to me is the craziest part. Soft cloth baby carrier use is banned because of a 1994 study that tested car seats -- meanwhile I am allowed to put my baby in their car seat in the plane for the full duration of the flight including takeoff and landing.
attaching a baby carrier / car seat to a vehicle seems easy, but a recent study showed that about half of US drivers had their seats installed incorrectly, and these are vehicles where the driver has unlimited time and resources to get it right.
I can't imagine that percentage goes up when strapped for time and under pressure during aircraft boarding.
In my experience they always stopped by to check that the seat was certified and that you knew how to install it. For aircraft install though it's usually simpler than a car because the only way to do it is a belt pass through.
I remember the very first time I installed a car seat, I rigorously followed the instructions, verifying each step both textually and by image. After that, we had it inspected by the local FD who said "you did it wrong" and rearranged it in a way that looked wrong to me (some detail with the straps and routing). I still don't know who did it right.
Same experience. My wife and spent more than an hour trying to get it all right, then went to the inspection facility, and they completely re-did it all. I now have teenagers, but still don't actually know how to install a seat correctly.
Maybe car seats have gotten easier but with my two young kids I've had to install and uninstall car seats dozens of times. 5 out 6 different car seats. It only takes like 2 minutes to do it right.
Isofix, click, it goes green. Some have an additional strap which goes over the top and clips on. I'm not sure how you can get it wrong unless you either don't check it's green.
The installation mode for planes is actually easier due to the standardization of the actual seat belts versus for cars the carriers will have different instructions depending on whether UAS is present, belt install, top tether, etc. In an aircraft there's really only one way to do it which is passing the belt through.
My experience has been that as long as your car seat has the right certification they are allowed and the flight staff do check both that it has the certification sticker and that you've installed then correctly. The installation mode for planes is typically significantly simpler than in a car because it's just the belt pass through and seat angle. There's nowhere to attach a top tether.