Public transport
We haven't even finished automating our existing public transport on dedicated travel ways yet. There are automated subway trains, so they're further along than Google is. But they haven't finished converting. Many trains still have human personnel.
New public transportation is expensive. For example, the California high speed rail system is currently projected to cost \$68.4 billion: https://en.wikipedia.org/wiki/California_High-Speed_Rail
And that's a replacement for just one road. Note that the federal government only spends \$80 billion on transportation. So if it bought one high speed rail segment a year, it would have hardly any money left for maintenance of the existing roads, already underfunded.
If we include local and state government spending on roads and water as well, we can get up to \$416 billion. That's still only enough for six segments even if we drop all spending on water, which is rather important. And that's only 3120 miles of travel way (six 520 mile segments). Note that the US currently has 2.6 million miles of paved roads. Even assuming that a million miles of that are redundant, we'd still need five hundred years to replace the existing road system.
Unless you are willing to increase spending on transportation construction by a lot, this seems totally infeasible. Who wants to wait five hundred years for automated transportation?
It's possible that high speed rail is more expensive to build than slower rail systems. Ohio's proposed more modest speed rail system was only expected to cost \$3.5 million per mile, not the \$140 million per mile of the California system. That's better. If we only double spending for twelve and a half years, we could replace the system. Of course, that system would also be more complex. Rail lines would cross each other. People would have to switch trains relatively frequently, almost as frequently as we switch roads. That complexity would bump up the cost again.
Also remember that we have to maintain the existing roads while we build the new system and maintain the new system going forward. And what do we do with the obsolescent roads? It will cost money to block them off or tear them up as well.
And note that this requires everyone to double the money spent on transportation. Sort of feasible for the federal government but difficult for local governments. A more reasonable alternative would have local governments maintain existing spending while the federal and state governments each put up enough for a new segment a year. That extends the process out another twenty-five years.
That assumes that the Ohio projections were correct. Note that the California numbers increased by a lot from initial projections. If we quintuple the Ohio projections (which is the kind of cost increases that were in the California project), we get amounts more like what California is showing. And that assumes that the current California projections aren't still underestimating the costs. Even only doubling the costs, that takes us out seventy-five years.
Automated roads
Automated roads that manage traffic are better at avoiding car to car accidents, but they are worse at everything else. For example, what if a child decides to run across the highway? The road's automation can't control the child. So cars running on that road need to have just as many sensors and ability for independent reactions as the Google car. Otherwise, they are less safe.
I think that automated roads are likely to occur at the end of the process rather than at the beginning. When many cars are automated, they'll start getting their own lanes like high-occupancy vehicles do now. They'll join in linked convoys so that most can shut off their motors and coast. But this requires cars to be automated first.
Another issue is that the automated roads would only work with automated cars. If you put regular cars on them then the automated cars have to handle non-automated traffic. So they require automated cars to function. And how do you get to the automated road? You'd have to take legacy roads to get there. So the automated cars could not require the automated road, which just gets us back to the Google car.
Google cars
The Google approach is the only one that works in the near term, that allows automated and non-automated cars to share the road. That allows automated cars to make it all the way from the initial location to the destination without switching vehicles. And most people won't buy if their car won't go everywhere they need to go.
The Google approach is clearly the most difficult to program, but tests show it to be feasible. If it's feasible, then it's easier in every other way.
There is no evidence that people are interested in increased public transport. It's inflexible, inconvenient, and expensive. Most people would prefer to take their cars with them rather than switch to public transport that runs on its schedule, not theirs. Also, public transport only works if you're going to a place covered by public transport. Many people aren't. You can drive to public transport, but you can't drive your car after you leave it.
The Google car approach is the most likely because it doesn't rely on other changes. It scales anywhere from one to a billion cars. The other approaches require a certain level of usage to function. It can also be implemented on an individual basis. A single individual can choose which car to drive. A single individual cannot choose to implement public transportation (unless really rich).
Without the Google car, we'll never get to the point of being able to use automated roadways. We also won't be able to make taxis cheap enough to make public transport practical in general, not just when traveling from and to urban locations. For most people, the Google car is the only method that they could use.