A good premise, though I'd strongly suggest a retrospective view looking at how cities have been shaped in the past, by automobiles, lifts, and other technologies, in technological and pre-technological eras.

Cities are dendritic or networked structures. They can be defined as a locus of points with connections between them, both physical (as with transport networks), or logical -- the financial, cultural, social, political, communications, and other links between nodes.

Cities are characterised by greater nodal density than non-urban areas. Cities provide a superlinear return to scale, Cf. work of Geoffrey West (Santa Fe Institute) and others.

This is subject to limitations, ultimately an irreducible inter-nodal cost factor. An example of this would be the disease risks of major cities such as London and New York in the mid-19th century. London actually had a net-negative population replacement rate, excluding in-migration. That is, the city could not replace its population faster than it was dying out. The principle cause was disease, quite notably cholera epidemics, responsible for deaths up of to 50,000 people annually. It took the creation of the London Sewerage System (1870) for this to be addressed.

A similar history can be told of New York City. It had its first sanitation canal by the 1840s, but didn't have its first sewage treatment plant until 1903, and was still regularly dumping raw sewage into the Hudson River in the 1970s. (It now does so ... only irregularly.)

http://toilet-guru.com/nyc-sewer-system.php

New York (and Chicago) also saw the first use of the lift (elevator), which decreased the cost of vertical real estate, along with structural steel. The consequence being that those cities built up. By the 1950s, cheap petrol and booming auto sales made horizontal space cheap, and subsequent cities built out, notably also the Chicago area (which had land to expand into), Los Angeles, San Jose, Atlanta, and the Washington / Alexandria region.

New limits were reached with smog and traffic congestion levels, in suburbs. At the same time, crime and social problems were driving middle-class and wealthy residents from city centres. Policing costs and requirements, as well as greenfield infrastructure developments made sprawl more attractive than densification.

Self-driving, potentially electric, vehicles affect these dynamics a few different ways.

They may allow for more effective roadbed utilisation. Given traffic density in many cities, this may well be limited, and still likely cannot meet to density of urban bus, light-rail, or subway / heavy-rail systems.

They should reduce the requirements on residential and destination parking, by shifting parking to non-central regions. Parking may become denser and/or less deterministic -- it's not necessary that a specific vehicle is extracted, only that some vehicle is extracted.

Utilisation costs of transport likely shift toward marginal rather than fixed costs. That is, much of the present cost of private transport is a sunk value, whilst a distance- or time-based rental front-loads the full direct cost. This may discourage casual travel.

Transport use is very unevenly distributed through the day. Peak-load requirements are either un-met, are responded to with demand-pricing, or require a large unutilised capacity in off-hours.

A likely development of a multi-tiered service-class offering, as with rail, air, or ship transport. The lowest-level tier offering will be intentionally disincentivised to foster utilisation of higher-level tiers, in a private-enterprise system.

Elements of the service might be more or less reliable than current private transport.

I suspect on balance that denser rather than less dense construction will be incentivised, though it's hard to account for all factors, or arising disincentives.