the problem with this is the same as the problem when police shoot people. when there's only one side left, justice tends not to occur.
I think you're being a little disingenuous. Most police are shooting people in self-defense (https://www.statista.com/statistics/585140/people-shot-to-de...). A minority of victims are actually innocent, and justice still does tend to occur in those specific situations. For instance, George Floyd's killer received a (presumably) just punishment.
Also, anecdotally, I hear quite a lot about family of deceased in wrongful police shootings suing police. Although I don't think the difficulty that a private citizen has getting justice after being wronged by a police department is really at all the same as most road accident situations.