My own take.
I would feel a lot LESS safe with a gun if it meant everyone else potentially had a gun
I feel MORE safe, not having a gun, knowing the chances of anyone else having one is SFA.
If an intruder breaks into my house armed with a baseball bat, I can still have a chance of defending myself. If I am allowed to have a gun, chances are he will too and it wouldn't be a baseball bat anymore, but a gun I have to defend myself against.
I would feel more safe if I have a gun and there is a good gun control and I know that other person with guns are also gone thru the good gun control and can be trusted with a gun and they know how to handle it.
That a pretty massive IF even for a fantasy land.
Also, I might be fine today and able to pass any check with flying colours. Tomorrow my life could turn upside down, lose everything, spiral into a deep depression and drink/drug away all my problems. No one is going to say I have to return those guns even if I would massively fail the checks with my new situation
The best a background checks does is basically say, this person at some point in their life passed a background check. There is no requirement after that to conduct yourself in a manner that would continue to see you pass background checks.
Also, with guns so prevalent, who is to say someone who didn't pass the check just didn't go out and steal one?