Maniac,
You're right that insurance is a contract. My point, though, is that insurance is only bought to cover actual liabilities. I don't buy insurance to cover what happens if somebody drowns in my neighbor's pool, because I'm not liable for that in the first place. One could say (much less reasonably than your idea), "We should make that happen! Make it mandatory to buy insurance for your neighbor's pool." But that doesn't make any sense -- buy insurance to cover.... WHAT? It only makes sense to talk of insurance after there is a liability for the insurance to cover, so you would have to create the liability first, and that would make (as I argued) little sense and, in any case, would be controversial.
Point 5 seems wrong to me, I must say. You say,
"5 ownership of uninsured guns becomes illegal, easier to take illegal guns out of circulation"
Why does it become easier? Ownership of illegal guns is already, well, illegal. Why on earth would it become easier just because it is in violation of one more law?
I'm not even really sure that this would have impacted the recent events in any way. So far as I can tell, the perp's mother in this case was a law-abiding gun owner who would probably have gotten great insurance rates. No?