Also, there are tremendous operating cost savings to a free at the point of use transit system. No ticket machines, turnstiles, the associated maintenance, ticketing staff, fare enforcement officers/police in places where there aren't turnstiles. Additionally, without turnstiles, people can enter and exit metro stations more quickly during peak service hours. On buses, the driver doesn't need to waste time dealing with payments.
It's cheaper to fund a public transportation system through taxation. Some may make the argument that why should people that don't use it have to pay for it? Well, since it's now included in your taxes, there's an incentive for you now to use it. For the wealthy that would never use it, I argue that they benefit from it. Their workers use the system to get to work, their customers use it to arrive at their businesses, students use it to get to school. These students use that education to become employees at those businesses.