Here's the actual status quo: after a decade of research into autonomous cars specifically (not to mention the decades of AI and systems research before that), we are barely at the point where a car can function safely with Level 2 autonomy, in good conditions.
These prognostications about eliminating traditional cars are assuming reliable Level 5 autonomy in all conditions. And unlike most software, you can't just get 99% of the way there and call it done. If you want to remove the steering wheel, it has to work ALL the time (or close enough to make no difference.) They say that 80% of the work is in the final 20% of the project? We haven't even finished the first 30% of the work yet.
Even more than that, nobody seems to be talking about the fact that to get this to work reliably, you basically need full general intelligence (unless you can manage to turn the road system into a closed system, like rail is). For example: following verbal or gestured instructions from a police officer or construction worker. We don't even have _theories_ on how to build intelligence like that, yet.
Will it happen eventually? Sure, probably, eventually. Will we get a lot of use out of Level 2 and Level 3 autonomy in the mean time? Already happening. Will we be taking robotic taxis in the next 20 years? No way, not with current approaches absent a breakthrough in general AI.