You can not have regulated rates and must-carry rules without a limited number of licenses. Restaurants, etc, of course do not have regulated rates or must-serve rules (note that must -carry includes things not related to discrimination based on the person, but also discrimination based on the profitabilty of the trip).
If you have regulated rates, must-carry rules, and unlimited participants then there only two ways to be profitable: get more fares, and cut costs. Getting more fares means competing for fares, and since you can't do it on price that leads to things like drivers cutting off other drivers to get to a fare, fake fares (Uber would never stoop to that, would they?), stopping in dangerous places to pick up a fare, etc. These things actually occurred when the number of cabs was not limited (NYT called it the 'Yellow Peril' because the streets were so dangerous because of the antics of cabs competing for fares).
The other way to increase profit is to cut costs, which leads to shoddy equipment maintenance and over-worked, under-qualified drivers.
People like you always make it seem like these regulations just appeared out of nowhere, fully formed, exactly as they are now. They didn't. They were all in response to real problems. And, thanks to Uber, you can see exactly what would happen in the absense of regulations. 'Surge pricing', refused trips, scheduling fake trips with a competitor, uninsured drives, etc. In short, every one of the problems that the regulations are there for.