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.