If you paid the true cost of the highway, it would probably be more than the train. For some reason we expect public transit to make a profit, which we don't expect of roads or even airports.
In fact there are plenty of proponents of "free" to the user public transport. A purely tax-powered system would enable more spontaneous usage. (An alternative might be a post-paid or pre-paid card system, with no/low sign-up fees)
Public transport is something tha advances all of society. Even those that take the car save money and time when other people are taking the public transport (as roads are less congested), so they are clearly obligated to chip in. In fact moreso, because taking public transport can be more of an inconvenience, than taking the car.
This is of course something that many drivers don't believe in, that they should pay others to take public transport. But they benefit the most from it.
That is also, why a truly private entity can never design and run a public transport system. It has to be tax funded and municipality owned.
The actual service and maintenance can be done by private enterprises. The rolling stock and track should be in public ownership.
You also want to have standardized equipment across the country, so you can swap rolling stock, keep contracts cheap and easily adapt improvements that work well in similar environments.
The problem with the US, is that you need an integrated public transit system for it to really show its strengths. This means that the intial outlay for a successful system is going to be immense - and adoption will likely take a moment.
Re computer cars: A computerized cars will most likely be able to avert accidents, by adapting to the situation in such a way, that no dangerous situations arise.
A well engineered system will stop the car if it is unsure of whether it is safe to procede. A sudden obstacle does not appear out of nowhere. Whatever put the obstacle in the cars way is clearly at fault.
I can't imagine a case where a well-engineered computer controlled car can end up in an accident, that is caused by "the computer". Either the system wasn't well engineered - in that case it's the manufacturers fault, much like any other system that fails due to faulty engineering, or the system has a mechanical fault - which can happen in a real car as well, with the same consequences. Otherwise external influences are at work, which cannot be protected against.
What do you expect an airplane in terminal approach to do, when there is suddenly an object in its way? The autopilot would probably follow ILS, as there is no forward radar ranging, and crash into it, unless the pilot choses some evasive action. But that object is probably some guy in his light airplane with the radio out - it's not like the pilot can do much, if he spots the other guy's intention too late.
I've never seen anyone blame a computer, it's always the engineers fault. And rightly so. Yet we design and run in production systems that are much more complex than self-driving cars. Most guided missiles these days are fully autonomous. We trust them...