Some of us had to take the hard math in our majors. In a perfectly competitive full information free market system with no barriers to entry and no externality costs nothing would have to be theorectically "subsidized". Unfortunately, we don't live in that ideal world, we live in the real world, without the benefits of truly "perfect" competition, with real externality costs, with real differences in competitive advantage, such as degree of substituitability or monopoly (which is often the case in viable transporation alternatives), and with incomplete information, and plenty of resultant market disttortions.

Since this is the state of the real world, we often use the math of cost benefit, and modern Marshallian analysis of marginal cost/marginal benefit, to assess the cost minimizing point of maximum benefit or utility. This is the same calculus as profit maximization, and allows us to identify where a subsidy is more likely to be justified.

It is always a social decision to sacrifice resources for various outcomes that the market, that due to these marekt "imperfections, may or may not supply things like "Amtrak" in adequate amounts. So our preferences do count, but it does not have to be just popularity contest, there are ways to make these decisions sensibly, with positive benefits, at a minimum subsidy level necessary to provide the service. We just live in a time where we often appear to wallow in willful ignorance and choose not to.