Self driving cars won't always be new though. The price of the technology will drop rapidly as they become mass produced. And there will always an economic advantage to renting vs owning. The cost of the car is effectively divided over several people instead of one.
I suspect that will not be the case. While public transportation may catch up on price (if the political will exists to push it there), I do think there will be a period of time where hailing a self driving car will be cheaper than some or most public transit options.
A robotaxi can take you to the local robobus hub, which drives you to the local robotrain point, whereupon a Just In Time (un)scheduled train will leave, as all journeys can be coordinated.
The issues with public transports are the same as with biking in the US: It works better when cities are really dense. Suburbs destroy the efficiency of public transport, biking, walking, inline skating, and any other non-car transportation.
See, that's the thing with Hacker News. A lot of people here think Silicon Valley is the center of the world and everywhere is just like us, when the fact, we are living in a little bubble and a lot of the US operates very differently.
You really mean "It's a myth that poor people drive in heavily populated cities.", in that case, you would be correct lol.