I bet not much, if any. There are many more significant scandals in recent automotive history that everyone has already forgotten about. Not many people are running down to their Kia lot based on their impeccable reputation, they're going there because they sell contemporarily styled cars with a decent feature set, accessible financing, and they're priced a few hundred bucks less than everyone else.
However, if you’re risky enough that no insurance company will touch you, but you are able to financially mitigate your risk to other drivers, many states will allow you to fulfill your legal insurance requirements by self-insuring. So it’s technically not correct (in many states) to say that you have to buy insurance. You usually just have to be able to prove you can afford the risk of a (minor to moderate) accident. For example, in California, you can deposit $35k at the DMV and drive with no insurance.