Agreed, the "cars become autonomous" problems are separate from the "autonomous cars means nobody owns cars anymore" ones.
I'm more optimistic about autonomy. It still seems like a crazy hard problem, but things are advancing so fast right now that it actually seems like they might get there.
But I don't see where the leap from "autonomous cars" to "shared cars" happens. The main obstacle there is simply personal: I don't think people want shared cars. People want autonomous cars (although they probably want the autonomy to be optional) so that hurdle is not a problem on that side.