There is a difference between could we start to install an automated system network wide tomorrow (almost certainly not) and could we over time make the network so that certain aspects could be automated leading to a point where automation is almost guaranteed (more certain, but not guaranteed).
Automated cars have a LONG way to go before they are universal, however their "brain" would have to be a LOT smarter than that required for an automated train. For instance, how do you program a computer to work on a narrow country lane with passing places?
However, much as people will say that they don't want driver less cars and/or will carry on driving themselves it is almost inevitable that if the systems work and prove to be as safe or safer than a typical driver that over time there will be things put in place to discourage people from driving themselves (i.e. reassessment every 10 years to prove you are still a competent driver, which given the fuss about older drivers being unsafe from some sectors could be relatively easy to start, especially given that taking away someones driving licence would no longer mean that they couldn't get about).
For the time being automated cars are likely to have short ranges on them, which would likely lead to a boost in rail travel for longer distance travel.
Automated cars would not just be a replacement for those who use a taxi, there are a lot of people who belong to car clubs for whom it could be useful.
I also think that our traditional view of what a car should be like could change with the introduction of automated cars, as why do you need one vehicle per passenger pod? Would it not be more efficient to have two or three passenger pods with a vehicle travelling along a route stopping to pick up and set down other passengers (more akin to a train or bus but with a very limited calling pattern), in doing so it may add some time to how long it would take to get from home to work but if enough vehicles did it that time lost could be made up by the fact that there were less vehicles using the roads. To encourage their usage these multi pod vehicles could be cheaper than a single pod system (with the company making up the shortfall by being able to charge more people to use it, i.e. single pod vehicle £20 journey cost, multi pod vehicle £15 journey cost but with the operator being able to also add in two additional journeys at £7).
It could see the return of a travelling trunk with passengers loading them up in advance of vehicle then picking them up. If they were weather tight then it could be possible for them to be automatically loaded onto the vehicle. This could make pick up/drop off times fairly quick. such trunks could also be self propelled with a range of (say) 500m so as to allow them to be easily moved. (Anyone else thinking of "the luggage" that Rincewind has in the Discworld novals???).
With no self drive vehicles there would be less need for central reserves and so there could be scope for a traditional motorway which has 3 lanes in each direction to become a 7 lane road with each lane being able to be used for traffic in either direction depending on the required demand (including provision for road works). As such you could have 5 lanes towards a city and 2 away from it in the morning peak, with the reverse being true in the evening peak.
With regards to the railways, it is likely to be slow and steady and so in 50 years time there are a lot less tasks a driver needs to worry about. Much in the same way that cars can detect wheel slip on one wheel and reduce power to just that one wheel, so trains could do the same when determining how fast to accelerate.
Trains would have a major advantage over cars in that one train could learn from the train in front (i.e. do I detect that I need more time to brake as the rails are icy, this information is logged and the next train there allows more time to break). Even on lower frequency services (say hourly) a train at 20:00 would report that it needed to do x, so the train at 21:00 when (say) the temperature has dropped could then think x was what was need an hour ago my temperature sensor shows a 5 degree fall in temperature since then, I'll best add in a margin of error as conditions are likely to have worsened.
Yes automation of the railways would cost a lot of money, but it is likely to be done on a slow creep method. As such it is likely to take a long time to come about, but I wouldn't be surprised if we started to see more systems being automated.