You can't actually give someone your life. Killing the perpetrator doesn't bring back the victim, it's just revenge. And revenge is never justice.
What benefits the victim more? Setting the perpetrator on fire, or making the perpetrator [carry insurance sufficient to] pay the victim the most accurate estimate we can make of the monetary value of the damage caused? I know people hate assigning dollar figures to human life, but in the absence of some technology capable of resurrecting the deceased, how else do you propose to compensate the victim's loved ones?
Then there is the key point that jail costs time which is proportional to the individual fined rather than the victim. In a proportional payment system there would be an even larger perverse incentive to get hit by moneyed people if the fine was in anyway punitive.
"But it costs society to incarcerate and is a net negative from the point after the accident on", Yes but we decided that prisoners shouldn't incur debt for being imprisoned for some very good reasons.
What of the victims? What benefits the victims more than giving them money after the fact is reducing the risk of it happening in the first place. A payment system has either a more harsh proportional punishment than the current system to decrease this happening further, or reckless driving will increase because it is more tenable for the drivers (or people are irrational when assessing jail time and money as punishment and the deterrent affect is not proportional).
So my main point is while I agree that it may be utilitarian to lower the cost to society after the fact there can be even more utility to play the ultimatum game before the event.