Except that we already have restrictions on who can buy firearms. Specifically, your assertion about making it more difficult for domestic abusers to purchase. They're already prohibited possessors.
Your "guns are cars" idea isn't new. It comes up every single time. Guns are a Constitutionally protected right. Cars are not.
If you're going to compare subjects then compare subjects as they actually are.
Apply your insurance idea to 1st Amendment rights. Does that seem reasonable to you? Legal? Possible? Even remotely a good idea? Because it's none of those things.
Constitutional rights cannot be subject to barriers to exercise. That's kinda the point of the Constitution, it doesn't give us those rights, it protects us from the government restricting those rights.
The only good idea you've presented is tax breaks/credits for safe storage purchases. Absolutely fantastic idea that has incredible support from gun rights organizations.
RE: Common Sense on Guns