I'd say that large amounts of parking will still be required in a TAAS future; all those AVs will need to be stored somewhere overnight when people aren't using them after all. What will change is that the parking won't need to be at destinations, so most parking will be in low value, out of the way areas. Parking in high demand areas like people's homes, workplaces, and commercial areas will be largely eliminated. The acres of mall and power centre parking lots will be opened up for development without needing expensive underground parking, which will reduce the cost of development. What property management companies and condo corporations will do with their enormous underground parking garages is a fascinating question.
If the AV/EV revolution drives down costs as much as people like Tony Seba predict, people who continue to own their own cars will be almost exclusively the very rich. For them, parking will be available as a limited, premium service and will be largely irrelevant to the average person.