Car vs. bicycle accidents typically result in serious injuries for the cyclist, even at low speeds. A cyclist who is wearing a helmet has more protection than one without, but it's also the only protection he or she has. The person in the car likely will not suffer any injuries, but the cyclist could be critically injured or even killed.
Police chases are a staple of movies and a semi-common occurrence in real life, something most people have watched on the news at night -- if they haven't seen one in person. When a driver decides to run, we expect the police to flip on the lights and the siren and give chase.
First and foremost, cyclists need to follow traffic laws. If that means they need to approach stop signs just like drivers do -- stopping completely before proceeding -- then that's the law they should follow.