Let's expand that. Let's name your hypothetical person, Bob. He's living on the edge financially, and decides to go without insurance.
Let's bring in another person, Alice. Alice is also not in great financial shape. But Alice is able to pay for insurance and follows all the rules. Alice has a small amount of savings, go Alice!
One day, Bob hits Alice. It causes medical issues for Alice. Alice might have insurance, but it's potentially still expensive for Alice. Because of her injuries she can't work for a few weeks. She works hourly, so now loses wages. Luckily with FMLA she won't necessarily lose her job, but she needed every paycheck. But it doesn't really matter, because her car is now gone. She can't drive to work anymore. She can't drive to groceries. She can't afford a car, as a huge chunk her savings went to cover those medical bills and missed paychecks. She's pretty SOL huh.
Sounds like we need to let Bob off the hook for inflicting all this on Alice. After all, he needed to drive without insurance.
No. We should just make it possible so Bob didn't need to drive in the first place instead of excusing his choice to still drive when he couldn't really afford it. We should structure the incentives so Bob doesn't want to drive if he can't afford it.
People driving without insurance ruin lives like Alice's all the time.