The main benefit foreseen for cities is that self driving cars would need far fewer parking spaces needed in the middle of urban areas, which is capacity that could be given over to extra lanes for more traffic capacity. Most cars are idle for over 20 hours a day, and just sit doing nothing. I think I read something like a third of all road space in cities is dedicated to parked vehicles.
I think that logic is flawed (and on a quick Google I can't find anything to back it up). You're correct that most cars are idle most of the time. However most of those cars spend their idle time either on residential streets or in car parks - and neither offer much prospect for reducing congestion via extra lanes:
- Most car parks could not usefully be turned into roads because they are the wrong shape: Squarish and don't lead anywhere
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- Getting rid of parked cars on residential streets would certainly make those streets far more pleasant, and would ease traffic flow somewhat on those streets, mainly by avoiding the problem of cars going in opposite directions unable to pass each other. It could also allow some one-way residential streets to go back to being 2-way. But the problem is, on the whole, residential streets are not where the big congestion problems are, so overall this isn't going to make much difference.
Off the top of my head, I can think of very few streets in centres prone to traffic jams where the main reason for congestion is parked cars narrowing the streets (And of those that I can think of, none are in central London, and for most of ones I know of, it tends to be cars parked for 5 or 10 minutes while people pop to the shops, or lorries or vans unloading, not cars parked for hours on end. Would self-driving vehicles really reduce that kind of parking?).
You have to remember too that the pinch points that cause the most congestion tend to be the junctions and traffic lights - and almost invariably on-street parking is already not permitted in those places (precisely because those are the pinch points!). And further, self-driving vehicles that are not parked will often be spending some of that time driving empty to their next customer - adding to congestion in the process.
Certainly on Googling, the main consensus seems to be that self-driving vehicles are likely to make congestion worse, not better, in cities, since without action by the authorities, their main impact is likely to be to cause a shift away from public transport, increasing the numbers of vehicles driving around the roads.