Yonah Freemark @ The Transit Politic makes a case for funding transit at the federal level from an equity perspective, basically arguing it is redistributionist: A Renewed Look at Federal Funding for Transit Operations :

“This review suggests therefore that there is considerable reason to be skeptical of decentralizing transit funding. Indeed, it indicates that a centralization of spending at the federal level could improve outcomes in terms of regional equity by allowing a redistribution of resources based on need rather than ability to pay.”

Without disputing his analysis, the question is whether the best way to help poor people is having the federal government fund transit capital projects in metropolitan areas with the ability to match. There are alternatives. The one I like best is giving poor people money and letting them choose what to spend it on. The one I like second best is giving poor people transportation vouchers and letting them choose what transportation to spend it on (presumably the newly higher transit fares is one of the options). It is not at all obvious that what the federal government is actually doing under the long-standing transit policy regime since the 1970s (giving politicians ribbon-cuttings) is effective at helping poor people get around.
The important distinction is whether the federal government should help local governments or help citizens directly with its limited budget. Arguments can be made for both. You can subsidize supply or you can subsidize demand (or some combination of the two). I prefer subsidizing demand on equity grounds as it is more directly serving the persons in need, more efficient in the resulting allocation of resources, and allows consumers maximum choice. The resulting investment outcomes I think would be quite different.