That is the basic idea of taxes: to redistribute money. The problem was a bit different though: people that need trains (like disabled people) were pushed out of trains and trams by tourists with bikes. I still really enjoyed not having to care about tickets as well.

Our roads are toll-free too and we want to encourage the use of trains.

I lived in SF before I lived in Germany. What you're describing is how BART works and it's trash.

Because we want to encourage people to take the train and discourage them using cars.

Yeah, the tax could be targeted, e.g. tax on gasoline, or on cars, with ICE cars needing to pay more (even though they're better, public transport is still the better way to prevent the climate catastrophe), but hey, the idea of any tax is probably horrifying tp the libertarians on HN...