You think market conditions will make taxis safer? Why do you think we have OSHA? Why do you think selling products with lead paint in them is illegal?
Restricting markets, so you can only use politician approved services is the exact opposite of helping the consumer.
Too expensive? Well I don't really have a choice....
No laws dictated these qualities, no legislation demanded this level of safety. These practices were conceived via market forces, and safety was a by product.
> ...in order to compete in a free market...
The entire point of Uber is that the taxi industry is not a free market, therefore the things necessary to compete in a theoretical "free market" are not relevant and can't be assumed to be why Uber is successful.
Uber uses roads that were designed to comply with government safety regulations and their drivers drive cars designed to comply with a different set of government safety regulations. Those regulations exist because experience has shown that they need to.
Unless I'm wrong you're arguing that Uber is safe and efficient because market forces made it so. It's efficient because of technological advances and it's safe literally to the extent required by law.
Because they've opted out of the regulations their competitors are subject to Uber could offer a a more dangerous and less efficient service than current taxi companies and still "compete".