You are going for a reduction to the absurd here, but what you are saying isn't actually that far off what is practical.
In general, many behaviours influence the chance of bad things happening. Eg getting behind the wheels of a car in the first place increases the chance of vehicular manslaughter (compared to walking).
Society can punish the probabilistically bad behaviour, or the bad outcome or any combination of the two (including none).
If the punishment is purely financial, and enforcement is certain and actors have deep pockets, it doesn't really matter which combination you pick.
You can emulate the deep pockets by requiring people to get insurance. Even if the law only polices the bad outcomes, a rational insurance company might want to police its customers behaviour. (Eg your health insurance gives you a discount, if you show them evidence of healthy habits. That's equivalent to charging people who fail to provide that evidence more, but the discount is more PR friendly.)
Both driving at all and drunk driving increase the chance of a person committing vehicular manslaughter. Societies largely allow driving, but ban drunk driving.
Drunk driving is dangerous, mainly because drunkards have slower reaction times and are more prone to taking risks. The more alcohol you have in your blood, the harsher the fines and punishment. But we typically don't check people's sober reaction times and risk appetite, and charge them more for driving sober.
It's all about trade-offs.
In the case of vehicular accidents, most people don't necessarily have deep pockets, and the damage of injuring or killing people can't be undone by paying money. However we eg still let old people drive, and only do something about them when they actually get involved in an accident.