> what gives the government the right to force said interference?
The fact that a majority of people for moral reasons do not want certain types of agreements to exist, for example selling yourself into slavery.
> is there any scientific evidence that government control over car rides is actually making us significantly safer?
Why are you limiting yourself to car rides? If goverment control over _any_ other common business field, say, pharmacy, building safety, water, roads, rail and air travel, is making it safer for customers, why would this oversight suddenly be useless for public transportation by cars? Or are you implying that goverment control over _any_ other service provided to the public is a scam too?
> how do we know that the government is not vulnerable to private interest
We dont. And it is even naive to assume they arent.
> Is it reasonable to expect that giving such immense power to a small group of people will lead to fair decisions?
Allowing a single company to disrupt a whole existing diverse industry is even more unreasonable, since all the power would shift to a even smaller group people you cant even elect. Allowing Uber to drive eveybody else out of the public transportation market is like letting Microsoft drive everybody else out of the personal computing market.