Controlling guns without controlling guns

Here are a couple of simple solution to the gun control problem without actually banning guns.
Do require a background check for the purchase of every single gun purchase and add a requirement that the person pass a mental exam prior to the purchase.
Before purchasing a gun, the purchaser must purchase liability insurance for each gun purchased. This requirement would clear a lot of guns off the street and in the woods because law enforcement would be required to ask for proof of insurance when stopping someone who has a gun.
Insurance companies would love this.
Lastly and this doesn't effect gun ownership in the least, ban the sale and possession of body armor to civilians.