There's also the fact that in even moderately busy systems, the amount of fares collected is not insignificant. As an example, New York's MTA: http://interactive.nydailynews.com/project/mta-funding/
$6B out of $15B is quite a lot of money. Raising taxes to cover $6B in lost revenue would be quite the feat. And why wouldn't that $6B be better put towards housing, or hospitals, or schools, or even better public transport services? It's generally better to make services more useful, than to just make existing subpar service free.
> New York State Department of Transportation Acting Commissioner Cathy Calhoun said the bridge is set to get $13 million in repairs to enhance safety for pedestrians, bicyclists and motorists.
This is just one intersection and definitely not at the heart of the city. Jewel Avenue Q64 bus is probably symbolic of New York politics. It is frustrating to see no bus for half an hour and then see three buses come together at the same time. However, we can't have a train here even if we somehow we're able to create/take over the land we need.
A $13 million bridge repair sounds expensive. But to replace that bridge with a BRT line (as one example) has an initial upfront cost of ~$40 million, and has a higher per-day maintenance cost too. To replace that bridge with a real subway line (which is probably what NYC would need to best serve riders) could easily be $160 million or higher.
Roads are the cheapest way to provide public transportation. Not necessarily the best way, but always the cheapest way.
If riders are only paying about 1/8 of the total cost, where do you suppose the rest is coming from?
https://le.utah.gov/audit/12_01rpt.pdf
As of 2010, riders paid about 13% of the total cost of public transit operation. (Page 7, heading "Farebox Recovery Has Improved Since 2006")