You misunderstand the billions a year it takes to keep the public roads functional, it's not burning funds when it's your money. This whole free market spin of "participating a bit" you're trying to put on this makes no sense at all. That's called taxes.

Public transport is underfunded and blocked by the car lobby, so it's too expensive for what it is. Cars aren't that expensive because theyre already heavily subsidized (and you ignore all the money that goes to maintaining it). Your math doesn't add up in the real world if you take the true costs of cars, and it adds up even less if countries didn't specifically design stuff for cars.

We shouldn't build entire cities based on the few who can afford to waste money on a car, and make travel extremely difficult for everyone who can't, even if public transport was a poverty thing. (it's not)