Passenger 389. I don't see anyone saying guns/ammo should not be allowed in checked luggage. Why bother as check-in and retrieval are in non-sterile areas. Any nut can access those areas at most airports with a loaded rifle over a shoulder and a pistol in a pocket loaded with one in the chamber.
No, more needs to be done to ensure that those with guns are sane, trained in their use and follow procedures to ensure the weapons are safe. Recurrent testing to ensure skills are maintained would be a very good thing. Yes, it would be a hassle but millions of pilots go through similar testing. It's the price they have to pay, most willingly
What worries me these days is the rising numbers of gun owners who are advancing in age and beginning to suffer from dementia. We can take away their driving licenses, but we can't touch their gun licenses.