One could require a receipt or proof of purchase for a safe or a lock when buying a gun.

That's why in CA they make you buy a lock. But I don't really know anyone that uses the one they had to buy.

That's intentional.

This means only rich or well to do people can own guns?

I was specifically addressing teenagers access to their parents guns, specifically to prevent school shootings.

I'm okay with storage laws in homes that are primary residences to minors. But I don't believe that any storage law on its own prevents it. There is no way to ensure it's being following once the gun is taken home. It's why I am much more in favor of trying to influence gun culture to make improper storage stigmatizing.

Like a car license. You may not be checked all the time, but every once in a while and it's a crime to not have it if you're driving.

Those with concealed carry licenses do get checked as they are to tell an officer when they are carrying. I wouldn't be against these laws being federal. As for just ownership, do you just check everyone if they have a license or only when the police see the gun? Or when they go shooting on public BLM land?

The analogy for driving breaks down because you can buy a car without a license. You just can't drive it on public roads. Though you can on private roads without a license.