Of course they could. All the regulations you mentioned are only there because the Taxi companies lobbied hard for them. Had they lobbied half as hard to have the regulations loosened they could have gotten any regulations they wanted. The taxi companies bet big on using regulation to entrench their position and avoid competition rather than on improving their product. History will tell if it was a good bet or not, but so far it isn't looking too good.
In reality, modern taxi regulations date back to the 1930s, when the prevailing view was that consumer protection was best served by a combination of limiting competition and government price regulation. This was all happening at around the same time as the government rate-regulated other transportation industries: busses, freight trucking, and airlines.