The problem with comparing accident rates for doctors and cars with guns is that of intentionality of purpose.
Cars and doctors are not seen as having a primary purpose as instruments of lethal force. Guns are seen as such, esp. by antigunners. Thus, the comparison is not compelling. Accidents from cars or doctors are sad but acceptable side effects of their positive use.
The self-defense argument works better, IMHO. Then, accidents might be seen as acceptable risk.
However, the strongest antigunners won't be moved by such letters. They have discounted the arguments. The battle is for the undecided politician or voter.