Regarding the other points (companies and organized crime loving this), you can also look at other countries where guns are illegal. Practice shows there are less fatal incidents there.
The only thing that facial recognition would help in my country would be those cases when licensed gun collector gets robbed and his guns taken by organized criminals. In that situation it would only slow down the illegal use of those guns. Therefore it would possibly ramp the price up to a point where manufacture of illegal guns becomes profitable.
Problems this would solve e.g.:
- Children using their parents' gun at schools
- People using multiple guns (e.g. Las Vegas shooting)
Children using their parents guns is pretty neatly tackled here in my country by mandatory gun safes.
A person at the shooting ground unlocks your guns with their FaceID. Then you can shoot with them using your own FaceID for, say, 30 minutes. If time runs out, you ask the guy at the shooting range to unlock them again.
It's an application of the two-man rule, [1].
Elephant hunters should be required to use low caliber revolvers, so the elephant has a better chance of killing them.