"How far can this race to the bottom go before our search for low costs starts to war with our sense of personal safety and social responsibility?"
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.
Taxi regulation for safety reasons increases the trust in taxis for people that don't know the area: tourists.
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.
I think generic laws/jurisprudence that, in a court, would find those companies guilty of negligence (and heavily punish them) if they hadn't performed standard checks before hiring[1], would be more than enough to convince every company to check.
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.