The technology is not the problem. I don't think it will be ready in the timeframe many have predicted, but it will get there.
The much bigger problems are social and political. People will want to own their own vehicles and will be reluctant to let others use them (damage risk, etc.). There's a comfort level of security with ownership that doesn't exist with true sharing. Need a car right now? I've got one. People will probably use autonomous vehicles for some of the same advantages transit has: time-savings by doing reading/work/whatever during their commutes.
I think it's just as likely that autonomous vehicles will increase congestion as much as it is that they will descrease it. They won't decrease parking considerably because all of those owned vehicles will have to park somewhere. They *may* shift parking to the outskirts of, say, downtown, but momentum is a killer. If traffic is a problem with single-occupant vehicles, what will it be like with *zero*-occupant vehicles? Moving parking further out makes that even worse. In addition, I think there's a real possibility that autonomous vehicles make sprawl worse, as a 45-minute commute doesn't look so bad when you can be productive during it. Be prepared to fight freeway expansion.
On the political side, the carmakers are going to promote ownership as much as corporately possible. Look for regulations on autonomous vehicles designed to promote ownership (liability laws, etc.). Also forget about upgrading your software -- you'll have to buy a new car.
On the plus side, if electrics make up a significant amount of the fleet, we'll see a lot more charging stations come online. I've been fairly amazed at the increase in stations even in the short two years we've owned our LEAF. Autonomous operation should provide a decent boost in range.
Truly autonomous transit vehicles would be a real boon (except for the operators) but concerns about making them work for the disabled are real. Also something will have to be done about safety/passenger misbehavior. There isn't a simple solution. I don't think we'll see them on regular-route service for quite some time. LRT, BRT and expression buses are real medium-term possibilities. The ATU will certainly demand a "safety officer" or some such thing on board, to make sure things are running smoothly. I doubt they would be paid less than an operator. If so, the advantages of autonomous vehicles become less clear.
I just was writing some of the same things you were saying - in terms of ride-share, Transportation as a System - taking over, I think it will be all about how cheap autonomous electric vehicles can get - and think tech advancments in computing, sensors, processing power, batteries etc shows use that will be very cheap. And then you get the fleet cars doing 10-12 trips a day instead 2-3 for individually-owned cars, or 100k miles a year - these ride-share hailed vehicles could get super cheap per trip. If they get down to less than $100 a month all-in for every trip you want to take in a city for most people that drive 10k miles a year....watch out.
Because, what really, really makes them cheap in denser places is reduced parking needs - not so much in the cost of the car, but the cost of all the parking people are providing. If residential and commercial developers can build with no parking and still get tons of demand (in fact maybe even a premium for nice walkable density zones and lower costs/rents because building for no parking reduces $/sf of the projects), then ride-shares will take over in those areas, as there would be no parking available, and those denser, no parking areas will spread. (Cheap ride-shares may even tend to clump things in even wide open places like suburbs - in the way that main streets, and built-up neighborhood central districts developed back before cars and elevators).
On parking and congestion - I think ride-share autonomous vehicles will not doubt increase number of trips by cars or smaller vehicles (vans, shuttles) because they will be cheap and easy to use. They will also no doubt poach from transit and biking (as Uber/Lyft already are doing). How much this makes density of cars on roads at any given peak times or how much all these more trips will decreases travel times - we shall see. The autonomous vehicles will make traffic more efficient, so the net might not be that bad, and if there is some sort of congestion pricing/surge pricing - that would serve to level out use away from peak demand.
I do think ride-share fleets in most cities will greatly reduce total number of vehicles, even if more car trips are happening.
And autonomous cars can park far more efficiently. Autonomous fleet vehicles could park super tight in lines of cars, an if they are ride-share, they order they park in the pack won't matter when everyone leaves work, ride-share cars can peel off out of tight pack of parked cars, one by one as people leave work. And the cars can all park say, a mile or two away, and starting driving back to where all the people are when they start leaving and demanding cars - got to love software and AI - so even with the same number of cars, parking area needed would be way less and far more optimized. And I firmly believe, there will also be less cars. So parking needs reduced.
Also, if public transit adjusts wisely, I see small shuttles running frequently on many more heavily used routes, as way to reduce amount of cars. Trains and big electric BRTs will still make sense for densest areas, routes with lots of congestion, but may other minor routes that are currently too expensive to run city bus routes on, would become economical to have, say 12- person shuttles coming every 5 minutes. Have enough easy on-off shuttles coming every 5 minutes, that cost next to nothing to ride, and that got priority over single-rider cars of any type, that would seriously eat away from individual car use and relieve congestion, even if you have to hop on and off a couple different shuttle routes to get where you going, if they were faster than cars and much cheaper.
And a whole subset of ride-share AEV cars or vans or shuttles could easily be designed to accommodate loading people in wheel-chairs, kids in strollers, people with bikes etc. - just have a ramp out the side or the back of the vehicle.