Are Street Parking Fines Inequitable?

A group of renters are protesting proposed increases for Los Angeles's street parking tickets. From the LA Times:

Renters' rights activists are taking aim at Los Angeles Mayor Antonio Villaraigosa's plan to increase parking tickets by $10 -- the sixth increase in seven years at City Hall.
Advocates for working-class families said they intend to speak out on the proposal Tuesday afternoon at the City Council's Budget and Finance Committee, which is set to consider possible changes to Villaraigosa's proposed budget. The city faces a $238-million shortfall.
Those activists are taking special aim at the proposal to charge $78 for parking violations on street-sweeping day, saying it unfairly hits those who live in high-density neighborhoods where spaces are scarce.

This is not a new argument. Here is a description of the effects of Santa Barbara trying to improve street sweeping a few years ago:

On Tuesday, when the City Council heard a status report on the street-sweeping program, the members generally praised the progress. But Council members Grant House and Helene Schneider touched on some issues of equity.
One is how the program, bankrolled mostly by parking tickets, seems to be subsidized by the poor. Parking tickets generate almost a cool $1 million every year — that’s three-quarters of the street-sweeping program’s annual budget of $1.3 million. (The rest comes from ballot measures B and D, for creeks and transportation, respectively.)  Meanwhile, Santa Barbara’s most heavily ticketed area is the Westside, one of its poorest neighborhoods.
“That means you’re really applying two kinds of standards,” House said. “There should be an equal treatment of the different neighborhoods.”

The reason the Westside is ticketed more is because there are more people per unit are fewer off street spaces, plus the free on street parking is used by downtown workers. So what is the treatment here? Clean streets or parking citations? Is it inequitable to charge people for parking (see this Cal State student resolution arguing that it is unfair for students to pay as much as everyone else)? Lots of people seem to think that anything other than cheap or free parking for all is socially undesirable regardless of the broader costs. Will the Bus Riders Union inspire a Street Parkers Union?