Self-driving cars as in with no driver at all, even as a backup? Surely being allowed to run a fleet of self-driving taxis is 10+ years away from being legal?
They're not a taxi service. This might seem like splitting hairs, but it's important. The car-for-hire industry just got good enough that it ate the taxi companies' lunch.
A taxi service can pick you up from the side of the road when you hold up your hand and whistle.
A car-for-hire service is where you call a company and ask for them to give you a ride from place A to place B.
It should be obvious from those two sentences why taxis are more regulated.
Now, with increasing technology (primarily universal smartphones), the need for taxis cruising the streets at random looking for hails has dwindled significantly. This still doesn't mean car-for-hire services are taxi companies.
It might be how you understand "taxi" but that's not relevant, any more than if a robotic factory was doing work with a lot fewer people and a critic can't understand why minimum wage laws don't apply to the assembly machines. In his mind "factory" is something that uses labor to produce goods so there must be some scam going on. But he just doesn't understand.
When you hold up your hand, you have no information on the person pulling over to pick you up. You don't know the rate, you don't know the safety records, you don't know anything about the driver. At the airport, I have even been ordered into cabs by police officers. The consumer has very little choice.
With a car-for-hire service, I can investigate the car service ahead of time. I can get an exact rate quote and say "yes" or "no." I can decide whether or not they are worth my trust, and if I don't like them I can hang up, open the Yellow Pages, and shop around to find another one/
The fact that you think "press a button on my phone" is just the same as "put my hand in the air" is the same misunderstanding as the guy who can't understand why the robots aren't paid minimum wage. "Could my mental model of what's going on be incorrect? Am I out of touch? No, it's the children who are wrong."
Try this: taxi companies and car-for-hire services have been regulated differently for 100 years. Were they wrong to have been regulated differently all along?
The "get into a car with a total stranger with whom I have no commercial relationship" market is vanishing along with its regulations. There is no law of nature or regulation that says we need to find a new industry to be regulated the same way.