Ubiquitin makes an excellent point by comparing guns to cars.
Instead if banning guns outright, the solution could be to require casualty insurance for anyone who wants to own a gun. The insurance company will have underwriters who evaluate the risk. Depending on the risk level, the underwriter can rate them up or reject them. If the prospective gun owner is rejected, they can try to find a different insurance company who is willing to assume the risk. It would be similar to casualty insurance for cars: X amount per victim, Y amount per incident. Each state would decide what levels of insurance are necessary – just as they do with car insurance.