The economics of self driving cars will ensure a rise in public transit usage.
A few years ago, I was helping my friend consider options for saving money. On the table was if they needed to keep their car. Most of their commute was via public transit. However we looked at the number of transits for which public transit was not viable per month (visiting friends on the other side of the metro area, running to stores), multiplied by the cost of using a ride share service. Comparing this number to the car payment, auto insurance, gas, and maintenance, it was no contest: even a few trips amortized the cost of the car and made it worth it.
Every trip has a cost in dollars, time, and externalities (causing congestion, environmental impact, etc). People will tend towards being efficient with those costs, judged by their relative importance to them personally.
The thing is, owning a car is mostly a fixed dollar cost per month. Once you pass the point where owning one is worth it for a few trips, the cost of additional trips is far less, while the time savings remain high. The only time I consider public transportation is when parking is a problem, as all other things considered driving is preferable.
Once self driving cars reach a point where they are closer to the amortized cost of a trip when owning a car, the tradeoffs start to change. Those who use their cars for few, but necessary, trips will be the first to ditch owning. I suspect many multi-car families will downsize to a single car. Once you get rid of your car, and are using self-driving cars for the trips where they are necessary, the question for every trip becomes "public transit, or self driving?" Different trips will have different ways they play out. However lot of people who are currently eating the cost of owning a car and might as well drive anyways will suddenly be able to save a few bucks by using public transit instead.
The final magic of all this is that if you're going anywhere more than a few minutes away, there are many other people going from approximately where you are, to approximately where you're going. The big killer in public transit speed is time. Time going to a common pickup point, time waiting for it to arrive, time spent not going on a direct route, time spent stopping for others to get on or off. With a sufficiently well used self driving car network, it could easily join a few rides together at a point nearby, and have self driving cars ready and waiting at the point near your destination. Two quick transfers, and that's it. If the self driving car app says "45 minutes, $20, or 50 minutes for $10", lots of people would save that $10. For destinations such as downtown, airport, sport stadiums, there's even only one transfer. Given car pool lanes and such, transferring to an express bus might actually be faster than driving directly.
Groceries are probably my number one reason to keep a car. I can ride busses to and from grocery stores, but the inconvenience level of not only lugging tons of bags to/from but also dealing with your typical city life on the journey makes just using the car immensely more palateable. I've basically driven once every other week for the last year; for everything other than groceries, I walk or take transit.
However, there are a bunch of potential one-off situations that make owning the car (or at least having it on hand) important, too. For example, what can you do when you need an emergency vet visit? You're probably not going to be calling a rideshare or taking a bus for that. Those what-ifs are also a big reason I still have a car, even though I don't technically need one.
What about traveling to one-off destinations that may be a couple of hours away and not accessible by public transportation, like a trail head for a hike? Such trips just never happen in your scenario?
If someone does this say, every weekend all summer long, it's likely that keeping one car in the family will still be economical.
Once self driving cars remove the inconvenience of the last mile and difficulty of coordination, mixed modes of transport start to become really convenient. In your scenario, you might take a self driving cab from a suburb house to a small transfer station, transfer to an express bug/shuttle, which then takes you to a car rental. This hypothetical car rental wouldn't make much sense today, but consider a rental in a small mountain town, renting out off-road capable vehicles. From there you could go on your hike. Though this solution would be a little slower and less convenient than driving directly - on the larger scale for many people dealing with this 2 times a year would be better than the costs of owning a vehicle. Plus for many people it doesn't make sense to own a large rugged vehicle for driving in cramped downtown spaces - using the right vehicle for the job becomes an awesome option.
More popular trailheads for which the drive is fully paved won't be the first area serviced by self driving cars, but would be eventually.
The meta-point is this: Many people survive today just fine without owning a car at all, so it's reasonable to assume that self driving cars will expand the circle of people who's use cases will be fully covered by self driving cars. This will definitely not be everyone as soon as self driving cars come out.
As this circle grows, various niches of transportation will reach a critical mass and be developed. Another example is transportation between major cities. Currently you have inconvenient greyhound busses, or the rare train in the US. Then once you get to your destination you have to deal with transportation within that city. Today it's just easier to drive a few hours, assuming you already own a car.
Why can't that be covered by self-driving cars? There will definitely be some places that are truly unmapped and out of bounds for self-driving cars, but common hiking entrances and exits shouldn't be a problem.
A few years ago, I was helping my friend consider options for saving money. On the table was if they needed to keep their car. Most of their commute was via public transit. However we looked at the number of transits for which public transit was not viable per month (visiting friends on the other side of the metro area, running to stores), multiplied by the cost of using a ride share service. Comparing this number to the car payment, auto insurance, gas, and maintenance, it was no contest: even a few trips amortized the cost of the car and made it worth it.
Every trip has a cost in dollars, time, and externalities (causing congestion, environmental impact, etc). People will tend towards being efficient with those costs, judged by their relative importance to them personally.
The thing is, owning a car is mostly a fixed dollar cost per month. Once you pass the point where owning one is worth it for a few trips, the cost of additional trips is far less, while the time savings remain high. The only time I consider public transportation is when parking is a problem, as all other things considered driving is preferable.
Once self driving cars reach a point where they are closer to the amortized cost of a trip when owning a car, the tradeoffs start to change. Those who use their cars for few, but necessary, trips will be the first to ditch owning. I suspect many multi-car families will downsize to a single car. Once you get rid of your car, and are using self-driving cars for the trips where they are necessary, the question for every trip becomes "public transit, or self driving?" Different trips will have different ways they play out. However lot of people who are currently eating the cost of owning a car and might as well drive anyways will suddenly be able to save a few bucks by using public transit instead.
The final magic of all this is that if you're going anywhere more than a few minutes away, there are many other people going from approximately where you are, to approximately where you're going. The big killer in public transit speed is time. Time going to a common pickup point, time waiting for it to arrive, time spent not going on a direct route, time spent stopping for others to get on or off. With a sufficiently well used self driving car network, it could easily join a few rides together at a point nearby, and have self driving cars ready and waiting at the point near your destination. Two quick transfers, and that's it. If the self driving car app says "45 minutes, $20, or 50 minutes for $10", lots of people would save that $10. For destinations such as downtown, airport, sport stadiums, there's even only one transfer. Given car pool lanes and such, transferring to an express bus might actually be faster than driving directly.