Why would this be? Why would you needing to jump through extra hoops to acquire your gun made it any harder for someone to subsequently break into your home and steal it? The biggest effect would be people giving up on making the purchase altogether because of the hassle (not because they’re no longer able to), so that there is no gun to be stolen, which is why there is such objections - it’s hassling people out of, effectively denying them, what’s considered their right, by making it too inconvenient to exercise that right.
And a vast majority of deranged gun owners do not present as being deranged at the time of their purchase, which could be years prior to them going crazy, and thus would’ve passed any additional restrictions anyways.
I understand there would be some effect, and just one life saved would technically make restrictions effective, but it’s not going to have anywhere near the effect that proponents keep trying to claim it will.