Gas Stations pay for themselves. Otherwise its also tax based.
Still completely free public transport is not a good idea instead of investing in a high quality offering. (Higher Frequencies, Better Vehicles, more dense network). Because People usually take the car because it is more convenient, its always more expensive than public transport.
And in the past, free offerings have just diminished people walking or taking the bicycle, but no shift Car>Public Transit
That was my Point, people who drive right now don't use Public Transport because it isn't convenient for them.
Instead of burning funds to make it free for People who are perfectly capable of paying 300€/Month for their Car, you should use it to expand the Networks (New Train/Tram/Bus Routes) and augment their quality (Longer Operating hours/ Higher Service Frequency) and let them participate a Bit in the Costs, so you can improve the Network even further. (If they we're able to pay 300€/Month for their Car, they can certainly pay 50-100€ for a monthly subscription too)