It's argued that in some cities public transport systems the price of the ticket doesn't cover the cost of its own infrastructure, the machines to buy them, the ones to validate them the salaries of the agents verifying, etc. It can be more cost effective to drop the concept of ticket and make it a free public service.

I agree with all that, but some central governments such as Turkey go to great lengths to make public transport a paid service. The best public transport is the free one indeed.