Your question assumes one of two things, either the self-driving car is driving far above the speed limit or it has no brakes, both of those are unreasonable assumptions. In the scenario you present, the self-driving car would brake.

Of all the alleged use cases for AI, self-driving cars are one of the few that actually make sense. If the technology can be developed to drive at least as safely as an unimpaired human driver (and real-world testing seems to indicate that they're actually safer than that), there is no more drunk driving. There are no more traffic tickets. Suddenly, law enforcement resources are freed up to actually fight crime and catch criminals instead of serving as revenue collection officers for the state. To me, that sounds like a much more useful thing than asking Siri to unlock your door or Alexa to tell you what movies are showing at the local theater.