You should try walking through a city with a freer market for taxis than you are used to. The externality of safety requires a heavily regulated market or you get freelancers and shell companies taking risks beyond their ability to cover.
People thought that too until they ended up in accidents in their Uber and suddenly discovered the issues arising when travelling in a commercial vehicle with no commercial insurance.
You fail to demonstrate how more of that free market fixes safety problems. If you are suggesting the normal solution, you will end up creating stacks of regulation to force people into "free markets" for services they should buy to offset externalities such as risk to 3rd parties, which will in turn seek ways to create new externalities to cut their costs. That stack of turtles can either collapse under its own weight and need to pay usury rates or not actually address many of the externalities, or both..