No, not like that. Trains work well for arterial routes that need to carry large volumes of people along predictable corridors at predictable times of day -- eg., for commuting. And yes America certainly needs to get better at investing in them.
But trains don't work at all well for serving smaller volumes of people moving in stochastic patterns at arbitrary times of day. Neither do buses. Cars serve this need very well -- they also generate massive negative externalities in the process, but they do serve this need.
Why should we care about "people moving in stochastic patterns at arbitrary times of day"? Transport planners call this "incidental travel," implying that it isn't really significant. But this is because transport planners don't have a good means of addressing it. In fact, incidental travel actually the majority of trips that people take: going shopping, visiting friends, going to the doctor's, eating out, etc. The balance is about 60/40 for incidental travel / commuting.
People own cars to serve this need, because nothing else will (unless you're in a mega-city that can afford to run high-frequency mass transport 24/7). Then, since car ownership is a sunk cost, people use their cars for commuting as well, where they're really sub-optimal.
Travel demand is an incredibly heterogeneous problem, which can only be addressed with a hierarchy of modes. That includes mass transport at fixed schedules, individual transport that is on-demand, and intermediate collective transport modes that currently doesn't really exist. Autonomous vehicles with 4-8 person capacities and demand-responsive routing would solve a broad class of transport problems that conventional public transport cannot -- and could do so without many of the negative externalities of private cars.
I've written much more on the subject, if you're interested: http://archive.podcar.org/blogs/nathan-koren/article/news/th...