You literally cannot get more unregulated than that. What is your vision here?
The nature of the market is that you need a large network of drivers to succeed. That network is a powerful barrier to entry. And it likely requires a lot of funding to achieve.
A government could foster more competition within the industry by funding new start-ups, in an effort to bring the market closer to free market status.
This is what China does with many of their industries, and they do it really well. Despite their "communist party" brand, they are actually doing capitalism much better than the US in many areas.
Mind you, it's not something I particularly disagree with, but the only way this works is by imposing regulations on the dominating market forces to prevent them from buying out the competition or using their network advantage to crush them. And regulation is considered the antithesis to a free market.
And if a monopoly were to form, it would step in.