Yes, safe storage has to be mandatory or it wouldn't make sense.
What would be a safe storage? A safe comes to mind.
If weapons are stored in a cupboard, there has to be a locking mechanism that isn't easily to bypass.
We can be rational here, and say how the argument of a cupboard door can be broken with an axe a hammer etc. But that's still significant effort and force needed.
Kids likely won't break into a cupboard that way, just to get a hand on dads or moms weapons.
To register any purchase is really also the way to go... With that said, it would automatically close the existing loopholes at gun shows.
If the gun gets stolen, I have to be held responsible to report it within no later than 48 hours. I'd prefer 24 hours.
If the storage situation is settled, theft should be minimized. And if it happens that I violated the safety regulations, I will be fined for a first time with no less than $1000. If the gun was used in a crime, then criminal charges may apply as well. That should counter the rampant straw purchases as well. One faces already criminal charges when caught with straw purchase. So it's only consequent to extend the punishment even further if such purchase leads to a crime.
Further more, I would like to see actual classes when one obtains a permit. Make 2 things mandatory as well. For once CPR course, and some course on the responsible handling of firearms.