As far as people want to give up state-"guaranteed" safety for a better price. The state shouldn't have any saying in how ready I am to take risks. Who is the state to tell me in whose car I sit to go from A to B? In this particular case, the state is only a hinderance for the market to adjust to the personal needs of people.
Harp about personal freedom and responsibility of the state all you want, but the regulation is for people that don't know the area and could get hurt by stepping into the wrong car. Because when the day occurs that a tourist is kidnapped or hurt because of this service, it will ruin the local industry. Uber may not care about the locals once it is sufficiently global (what's one city?), but the municipality does and this is precisely the reason why they're stepping in.
Regulations are not magic, they can't tell if someone is a rapist. All they can do is check the criminal records, which Uber also does[1].
Uber may do the checks voluntarily, but having no regulation means you wish for a company that can refuse to do so.