In most cities I've lived homeless people don't pay fares regardless. Considering fare enforcement is very expensive, I imagine making it completely free would be be cheaper. The Utopian in me imagines a struggling working class person saving a significant amount of money. To us, 200 or 400$ a month for public transportation isn't a big deal, but if your only making 2k a month that's a ton of money.
I already pay sky high taxes, I figure the city can pay for public transportation out of that.