but wouldn't the whole system be cheaper if it were paid for by taxes? because at that point you don't have to maintain a point of sale? hundreds of fare boxes, communication systems, physical barriers, auditing, accounting, printing cards, employees to maintain and operate it all... you even save a little time it takes tapping a card to get people on
the tax system is also progressive, so the people who are most capable of paying pay the most and the poor truly pay nothing
charging for a public system seems like pure waste
No, it's not even close. Those fares don't cover the whole operation of the train system, but they actually go a long way to covering a very large chunk of it. The cost of operating the fare system is a rounding error relative to the sums of money talked about here.