To the extent people previously paid for tickets, free public transportation does cost money of course. But that is not really a disadvantage: The people of Est

To the extent people previously paid for tickets, free public transportation does cost money of course. But that is not really a disadvantage: The people of Estonia gains just as much by not having to pay for tickets individually as they lose by paying for them collectively by way of their state. If the increased ridership necessitates an increase in capacity, that clearly does have a cost. But often, a route has much higher capacity than necessary in order to increase frequency or to keep the schedule more regular. No one should decide against using public transportation in such a case in order to save money. Making it free prevents that. Paying money to people is also effectively free for the state to the extent that they use it to purchase tickets for spare capacity of public transportation or other things the state provides that have zero marginal cost. But people almost certainly spend a smaller share of that on spare capacity than if they receive it as "tickets". So free public transport may not be free, but it is cheaper than paying people the money their tickets would have cost.