Free public transport takes away money that can be used to improve service for everyone. Someone on minimum wage would prefer a bus they can actually use to get to work rather than having to buy/maintain a car because the free bus only comes once an hour.
Have targeted low fares for the poor etc.
Go have a look what percentage of the operating costs are covered by fares in your city. I wouldn't be surprised if the costs relating to fare enforcement were more than the revenue from fares.
Of course it doesn't. The cost of public transport is a cost to society. It will be paid regardless of ticket fees. Hence the word 'public' in 'public transport'. The difference is that by making the users of public transport pay you give people a good reason not to use it when there are alternatives available. But those alternatives have a hard time competing with free.
https://en.wikipedia.org/wiki/Free_public_transport
It exists, and it works. And the best bit: all the money spent on the whole administration around tickets, making tickets, enforcing laws, gates and so on can be spent on improving the system.