Yonah Freemark at The Transport Politic writes A Note on Transportation Subsidies :

Why bring up these issues? Because Levinson describes a situation in which everyone has the option to pay the true cost of transportation services, but in fact many do not. A more efficient approach to ensure that people make the most cost-effective decisions might be one in which everyone got a reasonable amount of money to begin with, but we do not live in a particularly redistribution-inclined society.
So we are left with alternatives along the sidelines. We can crusade for the elimination of transportation services that cannot pay for themselves and in the process eliminate essential mobility for people who need to get around now, all the while hoping that the poor will at some point be handed adequate funds to make economically sound decisions. Or we can recognize reality and admit that transit services are at their core not just transportation organizations but also welfare providers.
This may be a disappointing conclusion, since it provides no insight as to how the state of funding for transit could be improved, but it does suggest that there is no way of getting around the fact that subsidies will continue to be needed in the running of public transportation unless some future technological advance reduces operations costs dramatically. There are plenty of ways to improve the performance and cost effectiveness of transit systems, but we cannot ignore the fact that transit plays an important redistributionist role.

Yonah is basically describing the problem of the first best and second best. He is arguing that because there are poor people, and society won’t give them enough money directly, we should subsidize services for them. Clearly that is what we do. But what should we do for the poor?
In my order of preference.
1. Give them money (a la Milton Friedman’s Negative Income Tax). It is a clean elegant solution that avoids distortions. Hence politicians don’t like it.
2. If you don’t trust the poor with money (and this seems to be society’s attitude, since we don’t actually give them money directly), give them transportation vouchers (e.g. top up their per use transit pass with $X per week, or give them a monthly pass, or some other mechanism). This can be discreet, so no one else would know who received vouchers, everyone would use the same pay-as-you-go card. It accomplishes the appropriate ends, without burdening the transit system with this welfare function. It also allows freedom to be spent on taxi or rental car as needed (if in cash-equivalent form), rather than just fixed-route transit. Just because some people are poor does not mean they don’t have other transportation needs.
3. Only as a last resort should we distort an entire transportation mode and drive it into perpetual “crisis” mode for the sake of subsidizing a subset of users.
I realize I am idealizing things a bit, but if we don’t idealize, we will never improve.
Just as roads are underfunded and we see congestion, because they are not priced properly and spending is too focused on expansion rather than preservation, a point that has been made numerous times on this blog, transit is underfunded and we see both crowding in some places and literally, (yes literally) empty buses in others, both of which are the consequence of severe misallocation of resources to achieve the what Jarrett Walker calls “coverage” aims.
I expect that the places that would see service dropped once you went to an appropriate funding model are not the poor inner-city areas, which are (or ought to be with appropriate management/regulation/etc.) profitable given the relatively high densities, but instead the suburban routes. In fact, the current model is largely a cross-subsidy from the poorer areas to the middle-class areas.
See Brian Taylor (1991) Unjust equity. Taylor’s abstract says:

Federal subsidies of public transit, particularly transit operations, are declining and the responsibility for supporting transit is falling increasingly on states and localities. In California, the Transportation Development Act (TDA) has become the state’s principal source of transit operating subsidies. It is found that the strict per capita allocation formulas of the TDA strongly favor lightly patronized suburban transit service over more heavily patronized service in the central cities. Transit riders in San Francisco, for example, receive a TDA subsidy of $0.13 per trip, whereas the TDA subsidy to transit patrons in suburban Livermore is over $5.00 per trip. The built-in suburban bias of the TDA is the result of partisan compromises made to secure passage of the Act in 1971–compromises to assuage a Republican governor opposed to new taxes–and to include the interests of rural and suburban counties. The result has been a proliferation in California of new, well-funded, and expanding suburban transit operators that attract few riders whereas older, heavily patronized central city transit operators are forced to cut service because of funding shortfalls. This paper concludes by proposing a more efficient and equitable method for allocating TDA funds than the current formula, which, in the name of equity, provides all Californians with a “fair share” of public transit whether or not they use it. [Emphasis added]

While the numbers have changed in 20 years, the basic observation stands.