There's also the more fundamental question of whether a public good like transit should (and can!) be run for profit and at the same time benefit the entire population and economy. It's possible that's only feasible in some cases, not others. (Of course, NY should be able to turn a healthy budget given the population density.. the mismanagement is evident)
I think, in general, this is one of the attributes of a well-run government institution. It just works and it doesn't draw attention to itself unless necessary to fulfill the job.
In my mind, these organizations are so ubiquitous, and so common, that it seems impossible to not identify them. However, the narrative of "government is bad" seems to be so powerfully blinding that I suppose they can be hard to identify for certain people.