It's true that politicians talking about shared values and ideals can turn simple private goods into nightmarish public ones (e.g. US medicine). Have politicians created dumb laws like "the conductor may not kick someone off the train even if they don't pay" or "long trips must cost the same as short ones"?
The train is merely an intermediate capital good used to provide train seats. It's private at the level of capital goods which is also the level at which it's paid for - only one railway can use a piece of rolling stock (rivalrous) and that railway can prevent other railways from using it (excludible). You might as well say that a house or a car is a public good, since they are merely capital goods that provide a stream of an underlying consumer good (space to live, road trips).
What are the positive externalities of a train? If anything, it's externalities seem to be negative - it creates pollution and noise. (It might be less negative than driving but that's a different claim.)
A train seat is not the thing I am paying for. A transit company is typically chartered around provision of service regions and schedules, and it has the power to divert passengers to alternatives like buses if problems arise preventing use of some existing infrastructure. The customer is not there to "ride the train" but to reach a destination - the transit is judged upon how well this demand is satisfied.
Private property law allows owners to enforce their own rules(to a point). This both explains the private control over the train and tracks and lends weight to the possibility of being kicked off the train, as it is justified in terms of disruption to service and resulting monetary losses. To wit, a positive externality of transit service is economic gain from the population having improved market access(more goods, services, workplaces within reach). The transit company does not realize these gains, the public does. The company's enforcement of rules is guided by the premise that some amount of security and order is necessary to achieve its service goals.
Reaching your destination via whatever mechanism is still a private good.
To wit, a positive externality of transit service is economic gain from the population having improved market access(more goods, services, workplaces within reach).
This is a positive externality of any transit method, including privately owned cars.
Ultimately what you've stumbled across is the fact that nearly any good or service will create gains from trade that are not captured by the producer. E.g., video games, cakes and pies, pornographic videos, and kindles all make people happier and nicer to those around them. This is why encouraging economic activity is generally considered beneficial.
Does this make cakes, pies, video games, pornos and kindles public goods?
The train is merely an intermediate capital good used to provide train seats. It's private at the level of capital goods which is also the level at which it's paid for - only one railway can use a piece of rolling stock (rivalrous) and that railway can prevent other railways from using it (excludible). You might as well say that a house or a car is a public good, since they are merely capital goods that provide a stream of an underlying consumer good (space to live, road trips).
What are the positive externalities of a train? If anything, it's externalities seem to be negative - it creates pollution and noise. (It might be less negative than driving but that's a different claim.)